Results 21 to 30 of about 7,090,364 (356)
Strong Maximum Principle for Viscosity Solutions of Fully Nonlinear Cooperative Elliptic Systems
Mathematics, 2021 In this paper, we consider the validity of the strong maximum principle for weakly coupled, degenerate and cooperative elliptic systems in a bounded domain.
Georgi Boyadzhiev, Nikolai Kutev
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Weak solutions of generated Jacobian equations
Mathematics in Engineering, 2023 We prove two groups of relationships for weak solutions to generated Jacobian equations under proper assumptions on the generating functions and the domains, which are generalizations for the optimal transportation case and the standard Monge-Ampère case
Feida Jiang
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On nonlinear Feynman–Kac formulas for viscosity solutions of semilinear parabolic partial differential equations [PDF]
Stochastics and Dynamics, 2020 The classical Feynman–Kac identity builds a bridge between stochastic analysis and partial differential equations (PDEs) by providing stochastic representations for classical solutions of linear Kolmogorov PDEs.
C. Beck +2 more
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Equivalence between distributional and viscosity solutions for the double-phase equation [PDF]
Advances in Calculus of Variations, 2020 We investigate the different notions of solutions to the double-phase equation - div ( | D u | p - 2 D u + a ( x ) | D u | q - 2 D u ) = 0 , -{\operatorname{div}(\lvert Du\rvert^{p-2}Du+a(x)\lvert Du\rvert^{q-2}Du)}=0, which is ...
Yuzhou Fang, Chao Zhang
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Regularity for convex viscosity solutions of Lagrangian mean curvature equation [PDF]
Journal für die Reine und Angewandte Mathematik, 2020 We show that convex viscosity solutions of the Lagrangian mean curvature equation are regular if the Lagrangian phase has Hölder continuous second derivatives.
Arunima Bhattacharya, R. Shankar
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User’s guide to viscosity solutions of second order partial differential equations [PDF]
, 1992 The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be
M. Crandall, H. Ishii, P. Lions
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Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility
Advances in Nonlinear Analysis, 2022 We consider density solutions for gradient flow equations of the form ut = ∇ · (γ(u)∇ N(u)), where N is the Newtonian repulsive potential in the whole space ℝd with the nonlinear convex mobility γ(u) = uα, and α > 1.
Carrillo J.A. +2 more
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Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues
Advances in Nonlinear Analysis, 2022 We consider the Dirichlet problem for partial trace operators which include the smallest and the largest eigenvalue of the Hessian matrix. It is related to two-player zero-sum differential games. No Lipschitz regularity result is known for the solutions,
Vitolo Antonio
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, 2014 Viscosity solution is a notion of weak solution for a class of partial differential equations of Hamilton-Jacobi type. The range of applications of the notions of viscosity solution and Hamilton-Jacobi equations is enormous, including common class of partial differential equations such as evolutive problems and problems with boundary conditions ...
Camilli, Fabio, Prados, Emmanuel
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