The probabilistic solution of the Dirichlet problem for \({1\over2}\Delta+\langle a,\nabla\rangle+b\) with singular coefficients

DOI10.1007/BF01060432zbMath0751.60071OpenAlexW1988070008WikidataQ114234103 ScholiaQ114234103MaRDI QIDQ1194476

W. D. Gerhard

Publication date: 27 September 1992

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01060432

zbMATH Keywords

Dirichlet problemweak solutioncontinuity principlegauge theoremexistence and uniqueness result

Mathematics Subject Classification ID

Probabilistic potential theory (60J45) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items

Neumann boundary value problems for elliptic operators with measure-valued coefficients ⋮ Harnack's inequality for parabolic operators with singular low order terms ⋮ Diffusion processes and second order elliptic operators with singular coefficients for lower order terms ⋮ A probabilistic approach to Neumann problems for elliptic PDEs with nonlinear divergence terms ⋮ Brownian motion with singular drift ⋮ Mixed boundary value problems of semilinear elliptic PDEs and BSDEs with singular coefficients ⋮ Dirichlet boundary value problems for elliptic operators with measure data ⋮ A probabilistic approach to mixed boundary value problems for elliptic operators with singular coefficients ⋮ Time-reversal and elliptic boundary value problems ⋮ A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients

Cites Work

• Uniform boundedness of conditional gauge and Schrödinger equations
• Extension of domains with finite gauge
• Green function for Schrödinger operator and conditioned Feynman-Kac gauge
• Harnack's Inequality for Schrodinger Operators and the Continuity of Solutions
• Potential theory for the Schrödinger equation
• Quadratic Variation of Potentials and Harmonic Functions
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