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<p>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 its stochastic representation, which can be viewed as a generalized nonlinear Feynman–Kac formula. From this representation we derive some additional regularity results for the solution and some uniqueness results.</p>

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Robin problems with measure data and singular nonlinearities on the boundary

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月25日

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  • Andrzej Rozkosz

摘要

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 its stochastic representation, which can be viewed as a generalized nonlinear Feynman–Kac formula. From this representation we derive some additional regularity results for the solution and some uniqueness results.