A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients

DOI10.1214/10-AOP591zbMath1242.60072arXiv1211.3820OpenAlexW2036957499MaRDI QIDQ717887

Tu-Sheng Zhang

Publication date: 10 October 2011

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.3820

zbMATH Keywords

weak solutionsquadratic formsbackward stochastic differential equationsDirichlet processesDirichlet boundary value problemsFukushima's decompositionmartingale representation theorem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Dirichlet forms (31C25) Applications of stochastic analysis (to PDEs, etc.) (60H30)

Related Items (6)

A probabilistic approach to Neumann problems for elliptic PDEs with nonlinear divergence terms ⋮ Backward stochastic differential equations and Dirichlet problems of semilinear elliptic operators with singular coefficients ⋮ Probabilistic representations of solutions of elliptic boundary value problem and non-symmetric semigroups ⋮ Mixed boundary value problems of semilinear elliptic PDEs and BSDEs with singular coefficients ⋮ Integral functionals under the excursion measure ⋮ The probabilistic solution of a system of semilinear elliptic PDEs under the third boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Adapted solution of a backward stochastic differential equation
• The probabilistic solution of the Dirichlet problem for \({1\over2}\Delta+\langle a,\nabla\rangle+b\) with singular coefficients
• Dirichlet forms and symmetric Markov processes
• Backwards SDE with random terminal time and applications to semilinear elliptic PDE
• Backward SDEs and Cauchy problem for semilinear equations in divergence form
• BSDE driven by Dirichlet process and semi-linear parabolic PDE. Application to homogeniza\-tion.
• Backward stochastic differential equations associated to a symmetric Markov process
• Diffusion processes and second order elliptic operators with singular coefficients for lower order terms
• Time-reversal and elliptic boundary value problems
• Stochastic calculus for symmetric Markov processes
• Perturbation of symmetric Markov processes
• Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
• Convergence of non-symmetric dirichlet processes
• From Brownian Motion to Schrödinger’s Equation
• Two-dimensional Brownian motion and harmonic functions

This page was built for publication: A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients