We consider a mixed linear parabolic problem with a second-order strongly elliptic operator and with dynamic boundary conditions, in a domain with smooth boundary Ω. For each β ∈ (0, 1), we determine necessary and sufficient assumptions on the data, so that there exist a unique solution u in C1+β/2,2+β((0, T )×Ω), with Dtu|(0,T )×∂Ω bounded with values in C1+β(∂Ω).

Linear parabolic problems with dynamic boundary conditions in spaces of Hölder continuous functions

GUIDETTI, DAVIDE
2016

Abstract

We consider a mixed linear parabolic problem with a second-order strongly elliptic operator and with dynamic boundary conditions, in a domain with smooth boundary Ω. For each β ∈ (0, 1), we determine necessary and sufficient assumptions on the data, so that there exist a unique solution u in C1+β/2,2+β((0, T )×Ω), with Dtu|(0,T )×∂Ω bounded with values in C1+β(∂Ω).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/597757
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