The Laplace operator on the Sierpinski gasket with Robin boundary conditions

DOI10.1016/J.NONRWA.2017.04.004arXiv1507.06209MaRDI QIDQ6263832

Ralph Chill, Brigitte Breckner

Publication date: 22 July 2015

Abstract: We study the Laplace operator on the Sierpinski gasket with nonlinear Robin boundary conditions. We show that for certain Robin boundary conditions the Laplace operator generates a positive, order preserving, $L^{i}nfty$-contractive semigroup which is sandwiched (in the sense of domination) between the semigroups generated by the Dirichlet-Laplace operator and the Neumann-Laplace operator. We also characterise all local semigroups which are sandwiched between these two extremal semigroups by showing that their generators are Robin-Laplace operators.

Mathematics Subject Classification ID

Operator theory (47-XX) Partial differential equations (35-XX)

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