Robin problem with measure data and singular nonlinearities on the boundary
Analysis of PDEs
2025-07-11 v1
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.
Keywords
Cite
@article{arxiv.2507.07821,
title = {Robin problem with measure data and singular nonlinearities on the boundary},
author = {Andrzej Rozkosz},
journal= {arXiv preprint arXiv:2507.07821},
year = {2025}
}