On the polygonal Faber-Krahn inequality
From MaRDI portal
Publication:6122616
DOI10.5802/jep.250arXiv2203.16409MaRDI QIDQ6122616
Publication date: 1 March 2024
Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.16409
Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Optimization of shapes other than minimal surfaces (49Q10)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators
- Universal extension for Sobolev spaces of differential forms and applications
- Krahn's proof of the Rayleigh conjecture revisited
- A proof via finite elements for Schiffer's conjecture on a regular pentagon
- Any three eigenvalues do not determine a triangle
- An introduction to Sobolev spaces and interpolation spaces
- Estimates for the deviation of solutions and eigenfunctions of second-order elliptic Dirichlet boundary value problems under domain perturbation
- Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
- A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions
- Eigenvalue stability bounds via weighted Sobolev spaces
- Domain perturbations and estimates for the solutions of second order elliptic equations.
- Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues
- Gagliardo-Nirenberg inequalities and non-inequalities: the full story
- A combined finite element and Bayesian optimization framework for shape optimization in spectral geometry
- Computing ultra-precise eigenvalues of the Laplacian within polygons
- Shape variation and optimization. A geometrical analysis
- An isoperimetric inequality for logarithmic capacity of polygons
- A note on the Sobolev and Gagliardo-Nirenberg inequality when \(p > N \)
- A counterexample to Payne's nodal line conjecture with few holes
- Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains
- Stability in shape optimization with second variation
- Positivity of the shape Hessian and instability of some equilibrium shapes
- Blaschke–Santaló and Mahler inequalities for the first eigenvalue of the Dirichlet Laplacian
- Verified Eigenvalue Evaluation for the Laplacian over Polygonal Domains of Arbitrary Shape
- Geometrical Structure of Laplacian Eigenfunctions
- Verification methods: Rigorous results using floating-point arithmetic
- Shape optimization and spectral theory
- Proof of the fundamental gap conjecture
- Sharp trace inequalities on fractional Sobolev spaces
- New Bounds for the Principal Dirichlet Eigenvalue of Planar Regions
- A Surgery Result for the Spectrum of the Dirichlet Laplacian
- SLEPc
- Coefficients of the Singularities for Elliptic Boundary Value Problems on Domains with Conical Points. III: Finite Element Methods on Polygonal Domains
- Estimates for Dirichlet Eigenfunctions
- Approximation of Ground State Eigenvalues and Eigenfunctions of Dirichlet Laplacians
- Serrin-type theorems for triangles
- New development in freefem++
- Symmetry results for variational energies on convex polygons
- Computation of Tight Enclosures for Laplacian Eigenvalues
- Stability Estimates for Resolvents, Eigenvalues, and Eigenfunctions of Elliptic Operators on Variable Domains
- Solving Laplace Problems with Corner Singularities via Rational Functions
- On Stein's extension operator preserving Sobolev–Morrey spaces
- 6 Triangles and Other Special Domains
- A lower estimation of the principal frequencies of simply connected membranes
- A proof of Saint-Venant's theorem on torsional rigidity
- Isoperimetric Inequalities in Mathematical Physics. (AM-27)
- Estimates of first and second order shape derivatives in nonsmooth multidimensional domains and applications
This page was built for publication: On the polygonal Faber-Krahn inequality
