Semilinear Dirichlet problem for subordinate spectral Laplacian
Ivan Biocic
TL;DR
This paper investigates semilinear boundary value problems involving non-local operators, extending spectral fractional Laplacian analysis, and explores harmonic functions and boundary behaviors of related potentials.
Contribution
It introduces new results on semilinear problems for non-local operators in bounded domains, extending spectral Laplacian theory and analyzing boundary behaviors.
Findings
Extended spectral fractional Laplacian analysis.
Characterized boundary behavior of Green and Poisson potentials.
Provided new insights into harmonic functions for non-local operators.
Abstract
We study semilinear problems in bounded domains for non-local operators with a boundary condition. The operators cover and extend the case of the spectral fractional Laplacian. We also study harmonic functions with respect to the non-local operator and boundary behaviour of Green and Poisson potentials.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Spectral Theory in Mathematical Physics