Stability in shape optimization with second variation
From MaRDI portal
Publication:2420507
DOI10.1016/j.jde.2019.03.033zbMath1416.49046arXiv1410.2586OpenAlexW2963938062WikidataQ128073898 ScholiaQ128073898MaRDI QIDQ2420507
Publication date: 6 June 2019
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1410.2586
Optimality conditions for problems involving partial differential equations (49K20) Optimization of shapes other than minimal surfaces (49Q10)
Related Items (16)
A quasi-Newton method in shape optimization for a transmission problem ⋮ Eigenvalues of Dirichlet Laplacian within the class of open sets with constant diameter ⋮ Quantitative Stability for Eigenvalues of Schrödinger Operator, Quantitative Bathtub Principle, and Application to the Turnpike Property for a Bilinear Optimal Control Problem ⋮ On the new coupled complex boundary method in shape optimization framework for solving stationary free boundary problems ⋮ On the polygonal Faber-Krahn inequality ⋮ Polygons as maximizers of Dirichlet energy or first eigenvalue of Dirichlet-Laplacian among convex planar domains ⋮ Why are the solutions to overdetermined problems usually ``as symmetric as possible? ⋮ Fuglede-Type Arguments for Isoperimetric Problems and Applications to Stability Among Convex Shapes ⋮ Quantitative inequality for the eigenvalue of a Schrödinger operator in the ball ⋮ On periodic critical points and local minimizers of the Ohta-Kawasaki functional ⋮ Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains ⋮ Asymptotic spherical shapes in some spectral optimization problems ⋮ Quantitative estimates for parabolic optimal control problems under \(L^\infty\) and \(L^1\) constraints in the ball: quantifying parabolic isoperimetric inequalities ⋮ Shape optimization of a Dirichlet type energy for semilinear elliptic partial differential equations ⋮ Uniqueness of the blowup at isolated singularities for the Alt-Caffarelli functional ⋮ Blaschke--Santaló Diagram for Volume, Perimeter, and First Dirichlet Eigenvalue
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Minimality via second variation for a nonlocal isoperimetric problem
- Stability of critical shapes for the drag minimization problem in Stokes flow
- La premiere valeur propre du Laplacien pour le problème de Dirichlet
- Some isoperimetric inequalities for membrane frequencies and torsional rigidity
- A mass transportation approach to quantitative isoperimetric inequalities
- Une méthode de comparaison isoperimetrique de fonctionnelles de domaines de la physique mathématique. I. Premiere partie: une demonstration de la conjecture isoperimetrique \(P\lambda^2\geq\pi j^4_0/2\) de Polya et Szegö
- Stable constant mean curvature surfaces minimize area
- Elliptic partial differential equations of second order
- A quantitative form of Faber-Krahn inequality
- A selection principle for the sharp quantitative isoperimetric inequality
- Isoperimetry and stability properties of balls with respect to nonlocal energies
- Zur Struktur der Lösungsmenge des Plateauproblems
- Second order optimality conditions and their role in PDE control
- Structure of shape derivatives
- Existence and stability for a non-local isoperimetric model of charged liquid drops
- Faber-Krahn inequalities in sharp quantitative form
- A sharp quantitative isoperimetric inequality in higher codimension
- The sharp quantitative isoperimetric inequality
- Sharp stability inequalities for the Plateau problem
- Variation and optimization of formes. A geometric analysis
- An isoperimetric result for the fundamental frequency via domain derivative
- A Strong Form of the Quantitative Wulff Inequality
- DETECTING AN OBSTACLE IMMERSED IN A FLUID BY SHAPE OPTIMIZATION METHODS
- Shapes and Geometries
- Necessary and Sufficient Conditions for a Local Minimum. 3: Second Order Conditions and Augmented Duality
- On the ersatz material approximation in level-set methods
- On Second Order Shape Optimization Methods for Electrical Impedance Tomography
- A strong minimax property of nondegenerate minimal submanifolds.
- About stability of equilibrium shapes
- Stability in the Isoperimetric Problem for Convex or Nearly Spherical Domains in R n
- On the first and second variations of a nonlocal isoperimetric problem
- Isoperimetric Inequalities in Mathematical Physics. (AM-27)
- Stable constant-mean-curvature hypersurfaces are area minimizing in small \(L^1\) neighborhoods
This page was built for publication: Stability in shape optimization with second variation
