Probabilistic interpretation of a system of quasilinear elliptic partial differential equations under Neumann boundary conditions

DOI10.1016/0304-4149(93)90109-HzbMath0789.60047MaRDI QIDQ1313129

Ying Hu

Publication date: 19 January 1994

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

Neumann boundary conditionbackward stochastic differential equationssecond order quasilinear elliptic partial differential equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Nonlinear boundary value problems for linear elliptic equations (35J65) Boundary value problems for higher-order elliptic equations (35J40) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60)

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A CLASS OF TWO-PARAMETER BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A BROWNIAN SHEET ⋮ Solution of forward-backward stochastic differential equations ⋮ A probabilistic approach to Neumann problems for elliptic PDEs with nonlinear divergence terms ⋮ Viability of moving sets for a nonlinear Neumann problem ⋮ Viscosity solutions for systems of parabolic variational inequalities ⋮ Optimal stochastic control with recursive cost functionals of stochastic differential systems reflected in a domain ⋮ A comonotonic theorem for backward stochastic differential equations in \(L^p\) and its applications ⋮ Mixed boundary value problems of semilinear elliptic PDEs and BSDEs with singular coefficients ⋮ A probabilistic approach to quasilinear parabolic PDEs with obstacle and Neumann problems ⋮ On the continuity of the probabilistic representation of a semilinear Neumann-Dirichlet problem ⋮ The probabilistic solution of a system of semilinear elliptic PDEs under the third boundary conditions ⋮ The stochastic counterpart of conservation laws with heterogeneous conductivity fields: application to deterministic problems and uncertainty quantification ⋮ A comonotonic theorem for BSDEs ⋮ A stochastic approach to a multivalued Dirichlet-Neumann problem ⋮ Generalized Reflected BSDE and an Obstacle Problem for PDEs with a Nonlinear Neumann Boundary Condition ⋮ Neumann boundary problems for parabolic partial differential equations with divergence terms

Cites Work

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• Adapted solution of a backward stochastic differential equation
• Multi-dimensional diffusion and the Markov process on the boundary
• Functional Integration and Partial Differential Equations. (AM-109)
• Probabilistic approach to the neumann problem
• Adapted solution of a backward semilinear stochastic evolution equation
• Probabilistic interpretation for systems of quasilinear parabolic partial differential equations

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