arXiv subjects

Brigitte E. Breckner

Publications and source records attributed to Brigitte E. Breckner.

2 recordsLinked to original sources

arXiv2016

On the existence of three solutions for the Dirichlet problem on the Sierpinski gasket

We apply a recently obtained three critical points theorem of B. Ricceri to prove the existence of at least three solutions of certain two-parameters Dirichlet problems defined on the Sierpinski gasket. We also show the existence of at least three nonzero solutions of certain perturbed two-parameters Dirichlet problems on the Sierpinski gasket, using both the mountain pass theorem of Ambrosetti-Rabinowitz and that of Pucci-Serrin.

math.AP↗

arXiv2015

The Laplace operator on the Sierpinski gasket with Robin boundary conditions

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.

math.FA↗