The Laplace operator on the Sierpinski gasket with Robin boundary conditions. (December 2017)

• Record Type: Journal Article
• Authors: Breckner, Brigitte E.; Chill, Ralph
• Is Part Of: Nonlinear analysis. Volume 38(2017)
• Page Start: 245
• Page End: 260
• Publication Date: 2017-12
• Subjects: Sierpinski gasket -- Laplace operator -- Robin boundary condition -- Nonlinear semigroups -- Dirichlet forms; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.04.004
• Languages: English
• ISSNs: 1468-1218

Abstract

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 ∞ -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.