Solvability of linear local and nonlocal Robin problems over \(C (\overline {\varOmega})\)
This paper is concerned with solvability of linear local and nonlocal Robin problems over \(C(\overline {\varOmega})\), where \(\Omega \subseteq \mathbb R^N\) is a bounded Lipschitz domain. Firstly, the author considers an elliptic boundary value problem with general Robin boundary conditions. The boundary conditions can be either local or nonlocal, depending on the conditions imposed on the elliptic operator. He proves that this boundary value problem is uniquely solvable, and moreover he shows that such weak solution is Hölder continuous on \(\overline {\varOmega}\). He also proves that a realization of the associated differential operator with generalized local or nonlocal Robin boundary conditions generates an analytic \(C_{0}\)-semigroup of angle \(\pi /2\) over \(C(\overline {\varOmega})\). He concludes by applying the elliptic regularity theory to solve the corresponding Cauchy problem over \(C(\overline {\varOmega})\).
local and nonlocal Robin boundary conditions
scientific article; zbMATH DE number 5966294
scientific article