Poincaré problem with measurable data for semilinear Poisson equation in the plane
DOI:
https://doi.org/10.15407/dopovidi2022.04.010Keywords:
Poincaré and Neumann boundary-value problems, measurable boundary data, logarithmic capacity, semilinear equations of the Poisson type, nonlinear sources, angular limits, nontangent pathsAbstract
We study the Poincaré boundary-value problem with measurable in terms of the logarithmic capacity boundary data for semilinear Poisson equations defined either in the unit disk or in Jordan domains with quasihyperbolic boundary condition. The solvability theorems as well as their applications to some semilinear equations, modelling diffusion with absorption, plasma states and stationary burning, are given.
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