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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
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
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
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
Journal Article
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
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
Journal Article
The Annals of probability, ISSN 0091-1798, 2016, Volume 44, Issue 2, pp. 1212 - 1253
Journal Article
Manuscripta mathematica, ISSN 1432-1785, 2018, Volume 159, Issue 1-2, pp. 247 - 268
We prove a global $$W^{1,\,\gamma (\cdot )}$$ W 1 , γ ( · ) -estimate for nonlinear non-uniformly elliptic problems on bounded smooth domains. More precisely,... 
Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 35D30 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 35K10
Journal Article
Duke mathematical journal, ISSN 0012-7094, 2000, Volume 102, Issue 2, pp. 253 - 271
Journal Article
Mathematische annalen, ISSN 0025-5831, 2012, Volume 356, Issue 1, pp. 99 - 146
We study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order $$\alpha \in (0,1)$$ . The... 
35R09 | Mathematics, general | Mathematics | 45K05 | 35K10 | MATHEMATICS | CONTINUITY | SPACES | DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | HARNACK INEQUALITY | HARMONIC-FUNCTIONS | VARIABLE ORDER | WEAK SOLUTIONS | NONLOCAL OPERATORS | VOLTERRA-EQUATIONS
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 12/2019, Volume 31, Issue 4, pp. 2061 - 2094
We study the blow up profiles associated to the following second order reaction–diffusion equation with non-homogeneous reaction: $$\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
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
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
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
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
Journal Article
Archive for rational mechanics and analysis, ISSN 1432-0673, 2018, Volume 230, Issue 2, pp. 493 - 538
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
Journal Article
Probability theory and related fields, ISSN 1432-2064, 2018, Volume 173, Issue 3-4, pp. 759 - 812
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
Journal Article
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