Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions

Nausica Aldeghi; Jonathan Rohleder

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arXiv · 2212.05889

Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions

Nausica Aldeghi·Jonathan Rohleder

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Abstract

The eigenvalue problem for the Laplacian on bounded, planar, convex domains with mixed boundary conditions is considered, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its complement. Given two different such choices of boundary conditions for the same domain, we prove inequalities between their lowest eigenvalues. As a special case, we prove parts of a conjecture on the order of mixed eigenvalues of triangles.

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BibTeX RIS

Nausica Aldeghi, Jonathan Rohleder. 2022-12-12. Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions. https://arxiv.org/abs/2212.05889

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