Advances in Mathematics, ISSN 0001-8708, 02/2018, Volume 325, pp. 1 - 33

We obtain a local Sobolev constant estimate for integral Ricci curvature, which enables us to extend several important tools such as the maximal principle, the...

Integral curvature bounds | Isoperimetric Constant | [formula omitted] Hessian estimates | Hessian estimates | MATHEMATICS | REGULARITY | FLOWS | L-2 Hessian estimates | RIEMANNIAN-MANIFOLDS

Integral curvature bounds | Isoperimetric Constant | [formula omitted] Hessian estimates | Hessian estimates | MATHEMATICS | REGULARITY | FLOWS | L-2 Hessian estimates | RIEMANNIAN-MANIFOLDS

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 10/2016, Volume 106, Issue 4, pp. 744 - 767

We establish sharp W2,p regularity estimates for viscosity solutions of fully nonlinear elliptic equations under minimal, asymptotic assumptions on the...

Regularity theory | Fully nonlinear elliptic equations | A priori [formula omitted] estimates | A priori W | estimates | MATHEMATICS | A priori W-2,W-p estimates | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | SPECIAL LAGRANGIAN EQUATIONS

Regularity theory | Fully nonlinear elliptic equations | A priori [formula omitted] estimates | A priori W | estimates | MATHEMATICS | A priori W-2,W-p estimates | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | SPECIAL LAGRANGIAN EQUATIONS

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 12/2013, Volume 100, Issue 6, pp. 785 - 805

Let (X,ω) be an n-dimensional compact Kähler manifold and fix an integer m such that 1⩽m⩽n. We study degenerate complex Hessian equations of the form...

[formula omitted]-subharmonic | Weak solution | Hessian operator | Kähler manifold | (ω, m)-subharmonic | MATHEMATICS | MATHEMATICS, APPLIED | (omega, m)-subharmonic | PLURISUBHARMONIC-FUNCTIONS | INEQUALITY | DIRICHLET PROBLEM | WEAK SOLUTIONS | Kahler manifold | MONGE-AMPERE EQUATION | Sects

[formula omitted]-subharmonic | Weak solution | Hessian operator | Kähler manifold | (ω, m)-subharmonic | MATHEMATICS | MATHEMATICS, APPLIED | (omega, m)-subharmonic | PLURISUBHARMONIC-FUNCTIONS | INEQUALITY | DIRICHLET PROBLEM | WEAK SOLUTIONS | Kahler manifold | MONGE-AMPERE EQUATION | Sects

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 04/2016, Volume 270, Issue 7, pp. 2691 - 2714

We establish an interior C2 estimate for k+1 convex solutions to Dirichlet problems of k-Hessian equations. We also use such estimate to obtain a rigidity...

[formula omitted] convex | Rigidity theorem | Interior [formula omitted] estimate | k-Hessian equations | estimate | Interior C | K-Hessian equations | K+1 convex | MATHEMATICS | Interior C-2 estimate | HYPERSURFACES | k+1 convex | EQUATION

[formula omitted] convex | Rigidity theorem | Interior [formula omitted] estimate | k-Hessian equations | estimate | Interior C | K-Hessian equations | K+1 convex | MATHEMATICS | Interior C-2 estimate | HYPERSURFACES | k+1 convex | EQUATION

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 04/2020, Volume 102, p. 106124

In this paper, we focus on the convergence analysis of the unique solution for a Dirichlet problem of the general k-Hessian equation in a ball. By introducing...

Unique solution | Radial solutions | [formula omitted]-Hessian equation | Error estimate | Convergence analysis | SCHRODINGER-EQUATIONS | EXISTENCE | EIGENVALUE | MATHEMATICS, APPLIED | k-Hessian equation | NONEXISTENCE | BOUNDARY-VALUE PROBLEM | FRACTIONAL DIFFERENTIAL-EQUATION | SYSTEM MODEL | MULTIPLE POSITIVE SOLUTIONS

Unique solution | Radial solutions | [formula omitted]-Hessian equation | Error estimate | Convergence analysis | SCHRODINGER-EQUATIONS | EXISTENCE | EIGENVALUE | MATHEMATICS, APPLIED | k-Hessian equation | NONEXISTENCE | BOUNDARY-VALUE PROBLEM | FRACTIONAL DIFFERENTIAL-EQUATION | SYSTEM MODEL | MULTIPLE POSITIVE SOLUTIONS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 02/2015, Volume 268, Issue 3, pp. 555 - 584

We consider fourth order elliptic systems in divergence form with greatly discontinuous coefficients in a nonsmooth domain. Our domain is composed of a finite...

Global [formula omitted] estimate | Composite Reifenberg domain | BMO space | Fourth order elliptic system | estimate | Global W | MATHEMATICS | PARABOLIC EQUATIONS | Global W-2,W-P estimate | NONSMOOTH DOMAINS

Global [formula omitted] estimate | Composite Reifenberg domain | BMO space | Fourth order elliptic system | estimate | Global W | MATHEMATICS | PARABOLIC EQUATIONS | Global W-2,W-P estimate | NONSMOOTH DOMAINS

Journal Article

Automatica, ISSN 0005-1098, 10/2014, Volume 50, Issue 10, pp. 2606 - 2614

We present the first q-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates...

[formula omitted]-Gaussian perturbations | Hessian estimate | Two-timescale algorithms | Stochastic optimization | q-Gaussian perturbations | APPROXIMATION | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Models | Algorithms | Mathematical optimization | Analysis

[formula omitted]-Gaussian perturbations | Hessian estimate | Two-timescale algorithms | Stochastic optimization | q-Gaussian perturbations | APPROXIMATION | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Models | Algorithms | Mathematical optimization | Analysis

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 01/2018, Volume 167, pp. 51 - 66

In this paper we study the k-convex solutions to the boundary blow-up k-Hessian problem Sk(D2u)=H(x)up for x∈Ω,u(x)→+∞ as dist(x,∂Ω)→0.Here k∈{1,2,…,N},Sk(D2u)...

[formula omitted]-convex solution | [formula omitted]-Hessian equation | Boundary blow up | Sub-supersolution method | k-convex solution | k-Hessian equation | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | 2ND-ORDER ELLIPTIC-EQUATIONS | BEHAVIOR | DIRICHLET PROBLEM | MONGE-AMPERE EQUATION

[formula omitted]-convex solution | [formula omitted]-Hessian equation | Boundary blow up | Sub-supersolution method | k-convex solution | k-Hessian equation | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | 2ND-ORDER ELLIPTIC-EQUATIONS | BEHAVIOR | DIRICHLET PROBLEM | MONGE-AMPERE EQUATION

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 01/2020, Volume 190, p. 111601

Consider the existence, nonexistence and global estimates of k-convex solutions to the boundary blow-up k-Hessian problem...

[formula omitted]-convex solution | [formula omitted]-Hessian equation | Boundary blow up | Weakly superlinear nonlinearity | Sub-supersolution method | EXISTENCE | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | k-Hessian equation | SEMILINEAR ELLIPTIC-EQUATIONS | BOUNDARY BLOW-UP | k-convex solution | ASYMPTOTIC-BEHAVIOR | UNIQUENESS | MATHEMATICS | DIRICHLET PROBLEM | SYSTEMS | MONGE-AMPERE EQUATION | REMOVABLE SINGULARITIES | Weighting functions | Hessian matrices

[formula omitted]-convex solution | [formula omitted]-Hessian equation | Boundary blow up | Weakly superlinear nonlinearity | Sub-supersolution method | EXISTENCE | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | k-Hessian equation | SEMILINEAR ELLIPTIC-EQUATIONS | BOUNDARY BLOW-UP | k-convex solution | ASYMPTOTIC-BEHAVIOR | UNIQUENESS | MATHEMATICS | DIRICHLET PROBLEM | SYSTEMS | MONGE-AMPERE EQUATION | REMOVABLE SINGULARITIES | Weighting functions | Hessian matrices

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 10/2019, Volume 64, Issue 10, pp. 1739 - 1755

We consider the Dirichlet problem for the complex Hessian equation of order . First, we give a specific estimate on the modulus of continuity of the solution...

Complex Hessian equation | O. Celebi | m-hyperconvex domain | m-subharmonic functions | 32W20 | 32U40 | 32U05 | 32T15 | MATHEMATICS | MONGE-AMPERE OPERATOR | HOLDER CONTINUOUS SOLUTIONS | DIRICHLET PROBLEM | Dirichlet problem | Formulas (mathematics) | Continuity (mathematics)

Complex Hessian equation | O. Celebi | m-hyperconvex domain | m-subharmonic functions | 32W20 | 32U40 | 32U05 | 32T15 | MATHEMATICS | MONGE-AMPERE OPERATOR | HOLDER CONTINUOUS SOLUTIONS | DIRICHLET PROBLEM | Dirichlet problem | Formulas (mathematics) | Continuity (mathematics)

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 01/2017, Volume 148, pp. 106 - 125

We prove an interior Lorentz estimate of the Hessian of strong solutions to fully nonlinear parabolic equations ut+F(D2u,x,t)=f(x,t) and elliptic equations...

Fully nonlinear parabolic equations | Fully nonlinear elliptic equations | [formula omitted]-vanishing nonlinearity | Lorentz spaces | Large-[formula omitted]-inequality principle | Large-M-inequality principle | (δ,R)-vanishing nonlinearity | EXISTENCE | MATHEMATICS | VMO COEFFICIENTS | MATHEMATICS, APPLIED | (delta, R)-vanishing nonlinearity | DIRICHLET PROBLEM | CONVEXITY ASSUMPTIONS | MEASURABLE COEFFICIENTS

Fully nonlinear parabolic equations | Fully nonlinear elliptic equations | [formula omitted]-vanishing nonlinearity | Lorentz spaces | Large-[formula omitted]-inequality principle | Large-M-inequality principle | (δ,R)-vanishing nonlinearity | EXISTENCE | MATHEMATICS | VMO COEFFICIENTS | MATHEMATICS, APPLIED | (delta, R)-vanishing nonlinearity | DIRICHLET PROBLEM | CONVEXITY ASSUMPTIONS | MEASURABLE COEFFICIENTS

Journal Article

Bulletin des sciences mathématiques, ISSN 0007-4497, 06/2017, Volume 141, Issue 4, pp. 267 - 311

In this paper, we introduce the first-order differential operators d0 and d1 acting on the quaternionic version of differential forms on the flat quaternionic...

Closed positive currents | Differential operators [formula omitted] and [formula omitted] | The Lelong number | The quaternionic pluripotential theory | Quaternionic plurisubharmonic functions | The quaternionic Monge–Ampère operator | and d | Differential operators d | MATHEMATICS, APPLIED | The quaternionic Monge-Ampere operator | PLURISUBHARMONIC-FUNCTIONS | Differential operators d and d | CAUCHY-FUETER COMPLEX

Closed positive currents | Differential operators [formula omitted] and [formula omitted] | The Lelong number | The quaternionic pluripotential theory | Quaternionic plurisubharmonic functions | The quaternionic Monge–Ampère operator | and d | Differential operators d | MATHEMATICS, APPLIED | The quaternionic Monge-Ampere operator | PLURISUBHARMONIC-FUNCTIONS | Differential operators d and d | CAUCHY-FUETER COMPLEX

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2018, Volume 509, pp. 140 - 150

We use the maximum q-log-likelihood estimation for Least informative distributions (LIDs) in order to estimate the parameters in probability density functions...

Maximum [formula omitted]-log-likelihood | Robust estimation | Score functions | Least informative distributions | Fisher information | Maximum q-log-likelihood | PHYSICS, MULTIDISCIPLINARY | GENERALIZED INFORMATION | ALPHA-BETA | DIVERGENCES | FIELD ISING-MODEL | CRITERION | SELECTION | PROBABILITY-DISTRIBUTION | TSALLIS STATISTICS | ENTROPY | Analysis | Distribution (Probability theory)

Maximum [formula omitted]-log-likelihood | Robust estimation | Score functions | Least informative distributions | Fisher information | Maximum q-log-likelihood | PHYSICS, MULTIDISCIPLINARY | GENERALIZED INFORMATION | ALPHA-BETA | DIVERGENCES | FIELD ISING-MODEL | CRITERION | SELECTION | PROBABILITY-DISTRIBUTION | TSALLIS STATISTICS | ENTROPY | Analysis | Distribution (Probability theory)

Journal Article

Pattern Recognition, ISSN 0031-3203, 2005, Volume 38, Issue 8, pp. 1239 - 1260

In this paper we describe a new shape-from-shading method. We show how the parallel transport of surface normals can be used to impose curvature consistency...

EM algorithm | formula omitted | Vector transport | Shape-from-shading | Surface curvature | surface curvature | PERCEPTION | shape-from-shading | SURFACE | vector transport | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms

EM algorithm | formula omitted | Vector transport | Shape-from-shading | Surface curvature | surface curvature | PERCEPTION | shape-from-shading | SURFACE | vector transport | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms

Journal Article

15.
Full Text
Genesis and evolution of velocity gradients in near-field spatially developing turbulence

Journal of Fluid Mechanics, ISSN 0022-1120, 03/2017, Volume 815, pp. 295 - 332

This paper investigates the dynamics of velocity gradients for a spatially developing flow generated by a single square element of a fractal square grid at low...

turbulent flows | turbulence simulation | turbulence theory | SKEWNESS | PHYSICS, FLUIDS & PLASMAS | ATMOSPHERIC SURFACE-LAYER | VORTICITY | FLOW | DIRECT NUMERICAL-SIMULATION | TENSOR | MECHANICS | REYNOLDS-NUMBER | ALIGNMENT | VELOCIMETRY | DERIVATIVES | Velocity gradients | Turbulent flow | Direct numerical simulation | Energy spectra | Fluid flow | Spatial discrimination | Turbulent wakes | Mathematical analysis | Dynamics | Vorticity | Wakes | Evolution | Eigenvectors | Mathematical models | Downstream | Stretching | Strain rate | Axial stress | Turbulence | Computer simulation | Computational fluid dynamics | Reynolds number | Fluid | Velocity | Velocity gradient | Equations | Strain | Studies | Dynamic tests | Numerical analysis | Vortices | Enstrophy | Decay | Inlets (waterways) | Spatial resolution | Formulas (mathematics)

turbulent flows | turbulence simulation | turbulence theory | SKEWNESS | PHYSICS, FLUIDS & PLASMAS | ATMOSPHERIC SURFACE-LAYER | VORTICITY | FLOW | DIRECT NUMERICAL-SIMULATION | TENSOR | MECHANICS | REYNOLDS-NUMBER | ALIGNMENT | VELOCIMETRY | DERIVATIVES | Velocity gradients | Turbulent flow | Direct numerical simulation | Energy spectra | Fluid flow | Spatial discrimination | Turbulent wakes | Mathematical analysis | Dynamics | Vorticity | Wakes | Evolution | Eigenvectors | Mathematical models | Downstream | Stretching | Strain rate | Axial stress | Turbulence | Computer simulation | Computational fluid dynamics | Reynolds number | Fluid | Velocity | Velocity gradient | Equations | Strain | Studies | Dynamic tests | Numerical analysis | Vortices | Enstrophy | Decay | Inlets (waterways) | Spatial resolution | Formulas (mathematics)

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 09/2018, Volume 63, Issue 9, pp. 1271 - 1289

We prove a global weighted Lorentz and Lorentz-Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation...

weighted Lorentz estimates | Fully nonlinear elliptic equations | Lorentz-Morrey spaces | viscosity solutions | weight functions | 35J60 | 35D40 | Lorentz–Morrey spaces | EXISTENCE | MATHEMATICS | PARABOLIC EQUATIONS | COEFFICIENTS | CONVEXITY ASSUMPTIONS | DOMAINS | Viscosity | Dirichlet problem | Nonlinearity | Nonlinear equations | Elliptic functions | Formulas (mathematics)

weighted Lorentz estimates | Fully nonlinear elliptic equations | Lorentz-Morrey spaces | viscosity solutions | weight functions | 35J60 | 35D40 | Lorentz–Morrey spaces | EXISTENCE | MATHEMATICS | PARABOLIC EQUATIONS | COEFFICIENTS | CONVEXITY ASSUMPTIONS | DOMAINS | Viscosity | Dirichlet problem | Nonlinearity | Nonlinear equations | Elliptic functions | Formulas (mathematics)

Journal Article

Journal of Statistical Computation and Simulation, ISSN 0094-9655, 03/2016, Volume 86, Issue 5, pp. 922 - 941

We investigate an analogue of the likelihood ratio test for spatial Gibbs point process models fitted by maximum pseudolikelihood or maximum composite...

Primary: 62F03 | Papangelou conditional intensity | score test statistic | variance estimation | pseudolikelihood | Secondary: 62M30 | 62-07 | Godambe-Heyde criterion | Georgii-Nguyen-Zessin formula | moment matching | Georgii–Nguyen–Zessin formula | Godambe–Heyde criterion | REGRESSION | PARAMETER-ESTIMATION | PATTERNS | STATISTICS & PROBABILITY | SIMULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | Null hypothesis | Computer simulation | Adjustment | Asymptotic properties | Mathematical analysis | Likelihood ratio | Statistical tests | Estimates

Primary: 62F03 | Papangelou conditional intensity | score test statistic | variance estimation | pseudolikelihood | Secondary: 62M30 | 62-07 | Godambe-Heyde criterion | Georgii-Nguyen-Zessin formula | moment matching | Georgii–Nguyen–Zessin formula | Godambe–Heyde criterion | REGRESSION | PARAMETER-ESTIMATION | PATTERNS | STATISTICS & PROBABILITY | SIMULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | Null hypothesis | Computer simulation | Adjustment | Asymptotic properties | Mathematical analysis | Likelihood ratio | Statistical tests | Estimates

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 7/2018, Volume 361, Issue 1, pp. 1 - 52

We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PARISI FORMULA | LOGARITHMIC SOBOLEV INEQUALITIES | GLAUBER DYNAMICS | COMPLEXITY | CONVERGENCE | MODEL | REM | CLOCK PROCESSES | PHYSICS, MATHEMATICAL | FREE-ENERGY | METROPOLIS DYNAMICS | Spin glasses | Analysis

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PARISI FORMULA | LOGARITHMIC SOBOLEV INEQUALITIES | GLAUBER DYNAMICS | COMPLEXITY | CONVERGENCE | MODEL | REM | CLOCK PROCESSES | PHYSICS, MATHEMATICAL | FREE-ENERGY | METROPOLIS DYNAMICS | Spin glasses | Analysis

Journal Article

ESAIM: Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 07/2017, Volume 23, Issue 3, pp. 827 - 850

We prove a generalization of the Li−Yau estimate for a broad class of second order linear parabolic equations. As a consequence, we obtain a new Cheeger−Yau...

Mathematical analysis | Formulas (mathematics) | Hyperspaces

Mathematical analysis | Formulas (mathematics) | Hyperspaces

Journal Article

Interfaces and Free Boundaries, ISSN 1463-9963, 2015, Volume 17, Issue 1, pp. 93 - 115

We consider equations with the simplest hysteresis operator at the right-hand side. Such equations describe the so-called processes "with memory" in which...

Sub-caloric functions | Free boundary | Monotonicity formula | Quadratic growth estimates | Hysteresis | REACTION-DIFFUSION EQUATIONS | MATHEMATICS | MATHEMATICS, APPLIED | monotonicity formula | quadratic growth estimates | sub-caloric functions | SPATIALLY DISTRIBUTED HYSTERESIS | hysteresis

Sub-caloric functions | Free boundary | Monotonicity formula | Quadratic growth estimates | Hysteresis | REACTION-DIFFUSION EQUATIONS | MATHEMATICS | MATHEMATICS, APPLIED | monotonicity formula | quadratic growth estimates | sub-caloric functions | SPATIALLY DISTRIBUTED HYSTERESIS | hysteresis

Journal Article