Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024468 | Nonlinear Analysis: Real World Applications | 2017 | 16 Pages |
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, Lâ-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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Authors
Brigitte E. Breckner, Ralph Chill,