Results 221 to 230 of about 87,102,086 (248)

On doubling properties for non-negative weak solutions of elliptic and parabolic PDE

Israel Journal of Mathematics, 2000
The paper studies quantitative properties for non-negative weak supersolutions for parabolic and elliptic PDE \[ \partial_t u-\operatorname {div}{\mathcal A}(t,x,u,\nabla u)+{\mathcal B} (t,x,u,\nabla u)=0\quad \text{in }(0,T)\times \Omega \] and \[ -\operatorname {div}{\mathcal A}(x,u,\nabla u)+{\mathcal B} (x,u,\nabla u)=0\quad \text{in }\Omega ...
openaire   +2 more sources

WEAK SOLUTIONS OF SEMILINEAR PDEs WITH OBSTACLE(S) IN SOBOLEV SPACES AND THEIR PROBABILISTIC INTERPRETATION VIA THE RFBSDEs AND DRFBSDEs

Stochastics and Dynamics, 2008
We prove the existence and uniqueness of the solution of a semilinear PDEs with obstacle(s) under Lipschitz condition. We give a probabilistic interpretation of the solution in Sobolev spaces using reflected forward–backward stochastic differential equations, doubly reflected forward–backward stochastic differential equations and the penalization ...
Ouknine, Youssef, Ndiaye, Djibril
openaire   +2 more sources

MATHER THEORY, WEAK KAM THEORY, AND VISCOSITY SOLUTIONS OF HAMILTON-JACOBI PDE'S

EQUADIFF 2003, 2005
We call the following three assumptions standard assumptions • H is convex in p, i.e. for all x ∈ T we have that the Hessian matrix ∂ pipjH(x, p) is positive definite for all p ∈ R. • H is superlinear in p, i.e. for all x ∈ T we have that lim H(x, p)/|p| → +∞ as |p| → +∞ • The flow defined by (1) is complete, i.e.
openaire   +1 more source

Weak and Measure-valued Solutions to Evolutionary PDEs: Introduction

Weak and Measure-valued Solutions to Evolutionary PDEs, 2019
J. Málek, J. Nečas, M. Rokyta, M. Růžička   +3 more
semanticscholar   +1 more source

New estimates for div-curl products and very weak solutions of PDEs.

1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Growth conditions and regularity for weak solutions to nonlinear elliptic pdes

Journal of Mathematical Analysis and Applications, 2021
Paolo Marcellini
exaly  

Weak Solutions to Fokker–Planck Equations and Mean Field Games

Archive for Rational Mechanics and Analysis, 2015
A. Porretta
semanticscholar   +2 more sources

Nonlinear Pantograph-Type Diffusion PDEs: Exact Solutions and the Principle of Analogy

Mathematics, 2021
Andrei Polyanin, Vsevolod Sorokin
exaly  

Methods for Constructing Complex Solutions of Nonlinear PDEs Using Simpler Solutions

Mathematics, 2021
Andrei Polyanin, Alexander Aksenov
exaly  

A method for constructing exact solutions of nonlinear delay PDEs

Journal of Mathematical Analysis and Applications, 2021
Andrei Polyanin, Vsevolod Sorokin
exaly