A shape variation result via the geometry of eigenfunctions

DOI10.1016/j.jde.2021.07.001zbMath1470.35021arXiv2009.13967OpenAlexW3091438878MaRDI QIDQ2048591

Yanyan Li

Publication date: 9 August 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.13967

zbMATH Keywords

mixed boundary conditionstorsional rigidityshape derivativefoliated Schwarz symmetrymonotonicity of the first eigenvalueZaremba problemgeometry of the first eigenfunctions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Maximum principles in context of PDEs (35B50) Invariance and symmetry properties for PDEs on manifolds (58J70) Optimization of shapes other than minimal surfaces (49Q10) Symmetries, invariants, etc. in context of PDEs (35B06) Comparison principles in context of PDEs (35B51) PDEs in connection with control and optimization (35Q93) Axially symmetric solutions to PDEs (35B07)

Related Items

On the optimization of the first weighted eigenvalue, Domain variations of the first eigenvalue via a strict Faber-Krahn type inequality, Strict monotonicity of the first \(q\)-eigenvalue of the fractional \(p\)-Laplace operator over annuli, Optimal shapes for the first Dirichlet eigenvalue of the \(p\)-Laplacian and dihedral symmetry, On the first Steklov-Dirichlet eigenvalue for eccentric annuli

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