Robin problem with measure data and singular nonlinearities on the boundary

2025/07/10 by Andrzej Rozkosz, Rozkosz, Andrzej
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2507.07821

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.

Citations

• On a nonlinear Robin problem with an absorption term on the boundary and L¹ data
• On a singular Robin problem with convection terms
• Doubly Feller property of Brownian motions with Robin boundary condition
• Semilinear elliptic equations with singular nonlinearities

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• On a nonlinear Robin problem with an absorption term on the boundary and L¹ data
• Boundary behavior of Robin problems in non-smooth domains
• Robin Problems of Elliptic Equations on Rough Domains: Hölder Regularity, Green's Functions, and Harmonic Measures
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