Positive solutions to semilinear Dirichlet problems with general boundary data

Lucian Beznea; Alexandra Teodor

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arXiv · 2312.00126

Positive solutions to semilinear Dirichlet problems with general boundary data

Lucian Beznea·Alexandra Teodor

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Abstract

We give a probabilistic representation of the solution to a semilinear elliptic Dirichlet problem with general (discontinuous) boundary data. The boundary behaviour of the solution is in the sense of the controlled convergence initiated by A. Cornea. Uniqueness results for the solution are also provided.

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Lucian Beznea, Alexandra Teodor. 2023-11-30. Positive solutions to semilinear Dirichlet problems with general boundary data. https://arxiv.org/abs/2312.00126

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