Convexity of domain functionals

DOI10.1007/BF02825640zbMath0052.33203MaRDI QIDQ2651312

M. M. Schiffer, Paul R. Garabedian

Publication date: 1953

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

partial differential equations

Related Items (76)

Dirichlet spectrum and heat content ⋮ On the conformal capacity of a spatial condenser with spherical plates ⋮ A mathematical analysis of Casimir interactions. I: The scalar field ⋮ The theory of the second variation in extremum problems for univalent functions ⋮ The Hadamard variation of the ground state value of some quasi-linear elliptic equations ⋮ A Morse Index Theorem for Elliptic Operators on Bounded Domains ⋮ On the Hadamard formula for nonsmooth domains ⋮ Convexity of functionals by transplantation ⋮ The effect of domain shape on the number of positive solutions of certain nonlinear equations ⋮ The Dirichlet principle for inner variations ⋮ Hadamard-type formulas via the Maslov form ⋮ The modulational regime of three-dimensional water waves and the Davey-Stewartson system ⋮ Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût ⋮ GeneralizedJ-integral and its applications I —Basic theory— ⋮ Second-order necessary conditions in a domain optimization problem ⋮ On the p-harmonic radii of circular sectors ⋮ On the strict monotonicity of the first eigenvalue of the 𝑝-Laplacian on annuli ⋮ Domain dependence of eigenvalues of elliptic type operators ⋮ Analytic characterization of monotone Hopf-harmonics ⋮ Hadamard's formula inside and out ⋮ Perturbation of domains and Green kernels of heat equations ⋮ Critical partitions and nodal deficiency of billiard eigenfunctions ⋮ Finite element analysis and shape optimization of singular points in boundary value problems for partial differential equations ⋮ Second domain variation for problems with Robin boundary conditions ⋮ A remark on the Hadamard variational formula ⋮ Liouville's formulae and Hadamard variation with respect to general domain perturbations ⋮ Remarks on Hadamard's variation of eigenvalues of the Laplacian ⋮ Perturbation of domains and Green kernels of heat equations. III ⋮ Hadamard variational formula for the Green's function of the boundary value problem on the Stokes equations ⋮ Brownian functionals on hypersurfaces in Euclidean space ⋮ Laplace eigenvalues on regular polygons: a series in \(1/N\) ⋮ Series in a Lipschitz perturbation of the boundary for solving the Dirichlet problem ⋮ Second-order derivative of domain-dependent functionals along Nehari manifold trajectories ⋮ An index theorem for Schrödinger operators on metric graphs ⋮ Prescribing harmonic measure on convex domains ⋮ Shapes of liquid drops obtained using symbolic computation ⋮ Shape derivatives for minima of integral functionals ⋮ New approach to the Hadamard variational formula for the Green function of the Stokes equations ⋮ Hypersurfaces in $\mathbb {R}^d$ and the variance of exit times for Brownian motion ⋮ Slit holomorphic stochastic flows and Gaussian free field ⋮ Second-order optimality conditions for constrained domain optimization ⋮ A free boundary problem in the theory of electrically actuated microdevices ⋮ Differentiability of potential energies with a parameter and shape sensitivity analysis for nonlinear case: the \(p\)-Poisson problem ⋮ Domain functionals and exit times for Brownian motion ⋮ The Hadamard variational formula for the ground state value of \(- {\Delta{}}u={\lambda{}}|{}u|{}^{p-1}u\) ⋮ Variational Formulas on Lipschitz Domains ⋮ Optimization algorithm for reconstructing interface changes of a conductivity inclusion from modal measurements ⋮ Boundary-variation solution of eigenvalue problems for elliptic operators. ⋮ The Calculus of Moving Surfaces and Laplace Eigenvalues on an Ellipse with Low Eccentricity ⋮ Variations of constrained domain functionals associated with boundary-value problems ⋮ Variation d'un point de retournement par rapport au domaine ⋮ On the lowest eigenvalue of the Laplacian with Neumann boundary condition at a small obstacle ⋮ Existence theorems, qualitative results and priori bounds for a class of non-linear Dirichlet problems ⋮ Well-posedness of the water-waves equations ⋮ A functional-analytic framework for the study of elliptic equations on variable domains ⋮ Variation of the Green's function due to quasiconformal distortion of the region ⋮ On the Placement of an Obstacle So As to Optimize the Dirichlet Heat Trace ⋮ On the second eigenvalue of the Dirichlet Laplacian ⋮ The Hadamard variational formula for the Green functions of some normal elliptic boundary value problems ⋮ Parameter and domain dependence of eigenvalues of elliptic partial differential equations ⋮ Concavity of condenser energy under boundary variations ⋮ How to place an obstacle having a dihedral symmetry inside a disk so as to optimize the fundamental Dirichlet eigenvalue ⋮ First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs ⋮ On a 'direct' method of proof of continuous differentiability of an extremal of a quadratic functional, relative to a parameter ⋮ A perturbation method in conformal mapping ⋮ A variational principle for waves of infinite depth ⋮ Variation of domain functionals ⋮ Hadamard Variation for Electromagnetic Frequencies ⋮ On Hearing the Shape of a Triangle ⋮ A remark on the Hadamard variational formula. II ⋮ On the normal variations of a domain ⋮ Imbedding annuli in C\(^2\) ⋮ On the spectrum of the Hecke groups ⋮ On differentiability of eigenvalues of second order elliptic operators on non-smooth domains ⋮ Asymptotic behavior of repeated eigenvalues of perturbed self-adjoint elliptic operators ⋮ A shape of eigenfunction of the Laplacian under singular variation of domains. II: The Neumann boundary condition

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• Über ein Minimumproblem für Potentialströmungen mit freiem Rande
• The Plateau problem for non-relative minima
• Axially symmetric cavitational flow
• Virtual Mass and Polarization
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
• Hadamard's Formula and Variation of Domain-Functions
• Continua of minimum capacity

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