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arXiv · 1507.06209

The Laplace operator on the Sierpinski gasket with Robin boundary conditions

Brigitte E. Breckner·Ralph Chill
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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, $L^\infty$-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.

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Brigitte E. Breckner, Ralph Chill. 2015-07-22. The Laplace operator on the Sierpinski gasket with Robin boundary conditions. https://arxiv.org/abs/1507.06209

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