Mathematische Annalen, ISSN 0025-5831, 12/2017, Volume 369, Issue 3, pp. 1623 - 1648

We prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form Eq $$\begin{aligned} u_t - F\left( D^2u, Du, X,...

35B65 | Mathematics, general | Mathematics | 35K10 | MATHEMATICS

35B65 | Mathematics, general | Mathematics | 35K10 | MATHEMATICS

Journal Article

Advances in nonlinear analysis, ISSN 2191-950X, 2019, Volume 9, Issue 1, pp. 7 - 15

The parabolic normalized p-Laplace equation is studied. We prove that a viscosity solution has a time derivative in the sense of Sobolev belonging locally to .

Non-linear equation | regularity theory | 35K92 | time derivative | 35K10 | MATHEMATICS | MATHEMATICS, APPLIED | 35k10 | 35k92 | non-linear equation

Non-linear equation | regularity theory | 35K92 | time derivative | 35K10 | MATHEMATICS | MATHEMATICS, APPLIED | 35k10 | 35k92 | non-linear equation

Journal Article

Communications in partial differential equations, ISSN 1532-4133, 2014, Volume 40, Issue 1, pp. 40 - 76

In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence...

Mean-field games | A priori estimates | Classical solutions | EXISTENCE | MATHEMATICS, APPLIED | 35J60 | 35A01 | 35K10 | 35A09 | MATHEMATICS | PDE METHODS | AVERAGE | SYSTEMS | ADJOINT METHODS | Partial differential equations | Linear equations | Interpolation | Hamilton-Jacobi equation | Inequalities | Games | Polynomials | Estimates | Regularity

Mean-field games | A priori estimates | Classical solutions | EXISTENCE | MATHEMATICS, APPLIED | 35J60 | 35A01 | 35K10 | 35A09 | MATHEMATICS | PDE METHODS | AVERAGE | SYSTEMS | ADJOINT METHODS | Partial differential equations | Linear equations | Interpolation | Hamilton-Jacobi equation | Inequalities | Games | Polynomials | Estimates | Regularity

Journal Article

MANUSCRIPTA MATHEMATICA, ISSN 0025-2611, 05/2019, Volume 159, Issue 1-2, pp. 247 - 268

We prove a global W-1,W-gamma(.)-estimate for nonlinear non-uniformly elliptic problems on bounded smooth domains. More precisely, we consider the following...

MATHEMATICS | 35D30 | 35K10

MATHEMATICS | 35D30 | 35K10

Journal Article

The Annals of probability, ISSN 0091-1798, 2014, Volume 42, Issue 1, pp. 204 - 236

In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs. This can also be viewed as viscosity solutions of...

Viscosity | Partial differential equations | Uniqueness | Differential equations | Mathematics | Mathematical vectors | Path dependence | Random variables | Coefficients | Stopping distances | Comparison principle | Path dependent PDEs | Backward SDEs | Functional itô formula | Viscosity solutions | functional Ito formula | STOCHASTIC DIFFERENTIAL-EQUATIONS | INFINITE DIMENSIONS | STATISTICS & PROBABILITY | NONLINEAR 2ND-ORDER EQUATIONS | viscosity solutions | backward SDEs | comparison principle | PARABOLIC PDES | 60H10 | 60H30 | 35D40 | functional Itô formula | 35K10

Viscosity | Partial differential equations | Uniqueness | Differential equations | Mathematics | Mathematical vectors | Path dependence | Random variables | Coefficients | Stopping distances | Comparison principle | Path dependent PDEs | Backward SDEs | Functional itô formula | Viscosity solutions | functional Ito formula | STOCHASTIC DIFFERENTIAL-EQUATIONS | INFINITE DIMENSIONS | STATISTICS & PROBABILITY | NONLINEAR 2ND-ORDER EQUATIONS | viscosity solutions | backward SDEs | comparison principle | PARABOLIC PDES | 60H10 | 60H30 | 35D40 | functional Itô formula | 35K10

Journal Article

The Annals of applied probability, ISSN 1050-5164, 12/2015, Volume 25, Issue 6, pp. 3095 - 3138

In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their...

Monte Carlo methods | Stochastic differential equations | Parametrix | Density | TRANSITION DENSITIES | STOCHASTIC DIFFERENTIAL-EQUATIONS | DIFFUSIONS | density | EXPANSION | LOCAL LIMIT-THEOREMS | STATISTICS & PROBABILITY | ERROR | stochastic differential equations | Mathematics - Probability | Probability | Mathematics | 65C20 | 65C30 | 35K15 | 65C05 | 35K10

Monte Carlo methods | Stochastic differential equations | Parametrix | Density | TRANSITION DENSITIES | STOCHASTIC DIFFERENTIAL-EQUATIONS | DIFFUSIONS | density | EXPANSION | LOCAL LIMIT-THEOREMS | STATISTICS & PROBABILITY | ERROR | stochastic differential equations | Mathematics - Probability | Probability | Mathematics | 65C20 | 65C30 | 35K15 | 65C05 | 35K10

Journal Article

Nonlinear differential equations and applications, ISSN 1420-9004, 2019, Volume 26, Issue 6, pp. 1 - 19

We consider the heat equation on a bounded domain subject to an inhomogeneous forcing in terms of a rate-independent (hysteresis) operator and a control...

Rate independence | Hysteresis operator | Heat equation | 47J40 | Analysis | Optimal control | Mathematics | 34K35 | Weak differentiability | 35K10 | MATHEMATICS, APPLIED | REGULARITY | NONSMOOTH

Rate independence | Hysteresis operator | Heat equation | 47J40 | Analysis | Optimal control | Mathematics | 34K35 | Weak differentiability | 35K10 | MATHEMATICS, APPLIED | REGULARITY | NONSMOOTH

Journal Article

The Annals of probability, ISSN 0091-1798, 2016, Volume 44, Issue 2, pp. 1212 - 1253

The main objective of this paper and the accompanying one [Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2012) Preprint] is to...

Viscosity | Partial differential equations | Stochastic processes | Uniqueness | Differential equations | Nonlinearity | Path dependence | Control theory | Dynamic programming | Stopping distances | Comparison principle | Path dependent PDEs | Second-order backward SDEs | Nonlinear expectation | Viscosity solutions | second-order backward SDEs | nonlinear expectation | STOCHASTIC DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | viscosity solutions | FORMULATION | BACKWARD SDES | comparison principle | 60H10 | 60H30 | 35D40 | 35K10

Viscosity | Partial differential equations | Stochastic processes | Uniqueness | Differential equations | Nonlinearity | Path dependence | Control theory | Dynamic programming | Stopping distances | Comparison principle | Path dependent PDEs | Second-order backward SDEs | Nonlinear expectation | Viscosity solutions | second-order backward SDEs | nonlinear expectation | STOCHASTIC DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | viscosity solutions | FORMULATION | BACKWARD SDES | comparison principle | 60H10 | 60H30 | 35D40 | 35K10

Journal Article

Manuscripta mathematica, ISSN 1432-1785, 2018, Volume 159, Issue 1-2, pp. 247 - 268

We prove a global $$W^{1,\,\gamma (\cdot )}$$ W 1 , γ ( · ) -estimate for nonlinear non-uniformly elliptic problems on bounded smooth domains. More precisely,...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 35D30 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 35K10

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 35D30 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 35K10

Journal Article

Duke mathematical journal, ISSN 0012-7094, 2000, Volume 102, Issue 2, pp. 253 - 271

Journal Article

Mathematische annalen, ISSN 0025-5831, 2012, Volume 356, Issue 1, pp. 99 - 146

We study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order $$\alpha \in (0,1)$$ . The...

35R09 | Mathematics, general | Mathematics | 45K05 | 35K10 | MATHEMATICS | CONTINUITY | SPACES | DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | HARNACK INEQUALITY | HARMONIC-FUNCTIONS | VARIABLE ORDER | WEAK SOLUTIONS | NONLOCAL OPERATORS | VOLTERRA-EQUATIONS

35R09 | Mathematics, general | Mathematics | 45K05 | 35K10 | MATHEMATICS | CONTINUITY | SPACES | DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | HARNACK INEQUALITY | HARMONIC-FUNCTIONS | VARIABLE ORDER | WEAK SOLUTIONS | NONLOCAL OPERATORS | VOLTERRA-EQUATIONS

Journal Article

Journal of Dynamics and Differential Equations, ISSN 1040-7294, 12/2019, Volume 31, Issue 4, pp. 2061 - 2094

We study the blow up profiles associated to the following second order reaction–diffusion equation with non-homogeneous reaction: $$\begin{aligned} \partial...

Non-homogeneous reaction | Self-similar solutions | 35B33 | Mathematics | Critical case | 35K67 | 35K10 | Blow up | Reaction–diffusion equations | Ordinary Differential Equations | 35Q79 | Applications of Mathematics | 35B40 | Phase space analysis | Partial Differential Equations

Non-homogeneous reaction | Self-similar solutions | 35B33 | Mathematics | Critical case | 35K67 | 35K10 | Blow up | Reaction–diffusion equations | Ordinary Differential Equations | 35Q79 | Applications of Mathematics | 35B40 | Phase space analysis | Partial Differential Equations

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2019, Volume 58, Issue 2, pp. 1 - 25

A singularly perturbed free boundary problem arising from a real problem associated with a Radiographic Integrated Test Stand concerns a solution of the...

35K20 | 35J61 | Systems Theory, Control | 35J60 | Theoretical, Mathematical and Computational Physics | Mathematics | 35J15 | 35K58 | 35J25 | 35K55 | 35K10 | Calculus of Variations and Optimal Control; Optimization | Analysis | MATHEMATICS | RADIAL SYMMETRY | MATHEMATICS, APPLIED

35K20 | 35J61 | Systems Theory, Control | 35J60 | Theoretical, Mathematical and Computational Physics | Mathematics | 35J15 | 35K58 | 35J25 | 35K55 | 35K10 | Calculus of Variations and Optimal Control; Optimization | Analysis | MATHEMATICS | RADIAL SYMMETRY | MATHEMATICS, APPLIED

Journal Article

Mathematische Annalen, ISSN 0025-5831, 2/2012, Volume 352, Issue 2, pp. 259 - 291

We take up in this paper the existence of positive continuous solutions for some nonlinear boundary value problems with fractional differential equation based...

34B27 | Mathematics, general | Mathematics | 35K10 | MATHEMATICS | GREEN-FUNCTION | Differential equations

34B27 | Mathematics, general | Mathematics | 35K10 | MATHEMATICS | GREEN-FUNCTION | Differential equations

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 2/2020, Volume 27, Issue 1, pp. 1 - 21

This paper presents a full classification of the short-time behavior of the interfaces in the Cauchy problem for the nonlinear second order degenerate...

Primary 35K55 | Mathematics | 35K59 | 35K57 | Nonlinear degenerate parabolic equations | 35K65 | 35K10 | Interfaces | Reaction–diffusion equations | Secondary 35R35 | Weak solutions | Analysis | Comparison theorem | Nonlinear diffusion | Mathematics - Analysis of PDEs

Primary 35K55 | Mathematics | 35K59 | 35K57 | Nonlinear degenerate parabolic equations | 35K65 | 35K10 | Interfaces | Reaction–diffusion equations | Secondary 35R35 | Weak solutions | Analysis | Comparison theorem | Nonlinear diffusion | Mathematics - Analysis of PDEs

Journal Article

Arabian Journal of Mathematics, ISSN 2193-5343, 3/2016, Volume 5, Issue 1, pp. 23 - 34

A numerical scheme combining the features of quintic Hermite interpolating polynomials and orthogonal collocation method has been presented to solve the...

65M70 | Mathematics, general | 35K05 | Mathematics | 65M60 | 35K57 | 35K10

65M70 | Mathematics, general | 35K05 | Mathematics | 65M60 | 35K57 | 35K10

Journal Article

Archive for rational mechanics and analysis, ISSN 1432-0673, 2018, Volume 230, Issue 2, pp. 493 - 538

We study the boundary regularity of solutions to the porous medium equation $${u_t = \Delta u^m}$$ ut=Δum in the degenerate range $${m > 1}$$ m>1 . In...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | DEGENERATE PARABOLIC EQUATIONS | MATHEMATICS, APPLIED | CONTINUITY | MECHANICS | NONLINEAR DIFFUSION EQUATION | BEHAVIOR | DIRICHLET PROBLEM | WEAK SUPERSOLUTIONS | LOWER SEMICONTINUITY | CRITERION | NONSMOOTH DOMAINS | Porous media | Dirichlet problem | Boundary value problems | Regularity | Cylinders | Mathematics - Analysis of PDEs

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | DEGENERATE PARABOLIC EQUATIONS | MATHEMATICS, APPLIED | CONTINUITY | MECHANICS | NONLINEAR DIFFUSION EQUATION | BEHAVIOR | DIRICHLET PROBLEM | WEAK SUPERSOLUTIONS | LOWER SEMICONTINUITY | CRITERION | NONSMOOTH DOMAINS | Porous media | Dirichlet problem | Boundary value problems | Regularity | Cylinders | Mathematics - Analysis of PDEs

Journal Article

Arabian Journal of Mathematics, ISSN 2193-5343, 12/2017, Volume 6, Issue 4, pp. 263 - 280

In this paper, we prove the existence of at least one periodic solution for some nonlinear parabolic boundary value problems associated with Leray–Lions’s...

35B10 | Mathematics, general | Mathematics | 35K59 | 35K10 | Exponents | Boundary value problems

35B10 | Mathematics, general | Mathematics | 35K59 | 35K10 | Exponents | Boundary value problems

Journal Article

Probability theory and related fields, ISSN 1432-2064, 2018, Volume 173, Issue 3-4, pp. 759 - 812

A first-order Liouville theorem is obtained for random ensembles of uniformly parabolic systems under the mere qualitative assumptions of stationarity and...

Statistics for Business, Management, Economics, Finance, Insurance | 35B27 | 35K40 | Parabolic system | Mathematical and Computational Biology | Liouville theorem | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | 35K10 | Parabolic equation | Stochastic homogenization | Operations Research/Decision Theory | Large-scale regularity | 35B53 | 60K37 | 60H25 | STATISTICS & PROBABILITY | Theorems | Ergodic processes

Statistics for Business, Management, Economics, Finance, Insurance | 35B27 | 35K40 | Parabolic system | Mathematical and Computational Biology | Liouville theorem | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | 35K10 | Parabolic equation | Stochastic homogenization | Operations Research/Decision Theory | Large-scale regularity | 35B53 | 60K37 | 60H25 | STATISTICS & PROBABILITY | Theorems | Ergodic processes

Journal Article

Computational Methods in Applied Mathematics, ISSN 1609-4840, 04/2019, Volume 19, Issue 2, pp. 283 - 293

We analyze a second-order accurate finite difference method for a spatially periodic convection-diffusion problem. The method is a time stepping method based...

65M15 | Operator Splitting | 86A10 | Convection-Diffusion | 65M06 | 35K10 | MATHEMATICS, APPLIED | Splitting | Diffusion | Diffusion coefficient | Convection-diffusion equation | Finite difference method

65M15 | Operator Splitting | 86A10 | Convection-Diffusion | 65M06 | 35K10 | MATHEMATICS, APPLIED | Splitting | Diffusion | Diffusion coefficient | Convection-diffusion equation | Finite difference method

Journal Article

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