Title: Dirichlet problem for semilinear partial integro-differential equations: the method of orthogonal projection.
Authors: Klimsiak, Tomasz; Rozkosz, Andrzej
Abstract: We study the Dirichlet problem for semilinear equations on general open sets with measure data on the right-hand side and irregular boundary data. For this purpose we develop the classical method of orthogonal projection. We treat in a unified form equations with operators belonging to the broad class of integro-differential operators associated with symmetric regular Dirichlet forms.
Subjects: SYMMETRIC operators; DIRICHLET problem; ORTHOGRAPHIC projection; INTEGRO-differential equations; OPERATOR equations
Publication: Calculus of Variations & Partial Differential Equations, 2025, Vol 64, Issue 1, p1
ISSN: 0944-2669
Publication type: Academic Journal
DOI: 10.1007/s00526-024-02860-z

Dirichlet problem for semilinear partial integro-differential equations: the method of orthogonal projection.

Klimsiak, Tomasz; Rozkosz, Andrzej