Robin problem with measure data and singular nonlinearities on the boundary

Andrzej Rozkosz

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arXiv · 2507.07821

Robin problem with measure data and singular nonlinearities on the boundary

Andrzej Rozkosz

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Abstract

We consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving blowing up terms. We prove the existence of a positive renormalized solution and provide it stochastic representation, which can be viwed as a generalized nonlinear Feynman-Kac formula. From this representation we derive some additional regularity results for the solution and some uniqueness results.

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Andrzej Rozkosz. 2025-07-10. Robin problem with measure data and singular nonlinearities on the boundary. https://arxiv.org/abs/2507.07821

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