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).
Guidetti, D. (2016). Linear parabolic problems with dynamic boundary conditions in spaces of Hölder continuous functions. ANNALI DI MATEMATICA PURA ED APPLICATA, 195, 167-198 [10.1007/s10231-014-0457-8].
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).File in questo prodotto:
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