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Boundary value problems --- Mathematical physics --- Maxima and minima --- Problèmes aux limites --- Physique mathématique --- Maxima et minima --- Maxima and minima. --- Boundary value problems. --- Mathematical physics. --- Problèmes aux limites --- Physique mathématique --- Minima --- Mathematics --- Physical mathematics --- Physics --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Initial value problems

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Problems linking the shape of a domain or the coefficients of an elliptic operator to the sequence of its eigenvalues are among the most fascinating of mathematical analysis. In this book, we focus on extremal problems. For instance, we look for a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. We also consider the case of functions of eigenvalues. We investigate similar questions for other elliptic operators, such as the Schrödinger operator, non homogeneous membranes, or the bi-Laplacian, and we look at optimal composites and optimal insulation problems in terms of eigenvalues. Providing also a self-contained presentation of classical isoperimetric inequalities for eigenvalues and 30 open problems, this book will be useful for pure and applied mathematicians, particularly those interested in partial differential equations, the calculus of variations, differential geometry, or spectral theory.

Eigenvalues. --- Maxima and minima. --- Valeurs propres --- Maxima et minima --- Eigenvalues --- Elliptic operators --- Maxima and minima --- Elliptic operators. --- Algebra --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- EPUB-LIV-FT SPRINGER-B --- Minima --- Differential operators, Elliptic --- Operators, Elliptic --- Mathematics. --- Operator theory. --- Potential theory (Mathematics). --- Operator Theory. --- Potential Theory. --- Partial differential operators --- Matrices --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Functional analysis

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Functional analysis --- Monotonic functions --- Maxima and minima --- Duality theory (Mathematics) --- Monotone operators --- Calculus --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Dualiteit [Theorie van de ] (Wiskunde) --- Dualité [Théorie de la ] (Mathématiques) --- Fonctions monotones --- Functies [Monotoon ] --- Functions [Monotonic ] --- Mathematics duality theory --- Maxima en minima --- Maxima et minima --- Monotone functies --- Monotone operatoren --- Opérateurs monotones --- Theorie van de dualiteit (Wiskunde) --- Théorie de la dualité (Mathématiques) --- Opérateurs monotones --- Dualité, Principe de (Mathématiques) --- Functional analysis. --- Operator theory. --- System theory. --- Calculus of variations. --- Functional Analysis. --- Operator Theory. --- Systems Theory, Control. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Systems, Theory of --- Systems science --- Science --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Philosophy --- Monotone operators. --- Algebra --- Mathematical analysis --- Topology --- Operator theory

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Theory of extremal problems

Mathematical optimization --- Maxima and minima --- Calculus of variations --- Extremal problems (Mathematics) --- Optimisation mathématique --- Maxima et minima --- Calcul des variations --- Problèmes extrémaux (Mathématiques) --- 519.85 --- 681.3*F22 --- 681.3*G16 --- Minima --- Mathematics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Graph theory --- Problems, Extremal (Mathematics) --- Geometric function theory --- Isoperimetrical problems --- Variations, Calculus of --- Mathematical programming --- Nonnumerical algorithms and problems: complexity of proof procedures; computations on discrete structures; geometrical problems and computations; pattern matching --See also {?681.3*E2-5}; {681.3*G2}; {?681.3*H2-3} --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Extremal problems --- Calculus of variations. --- Mathematical optimization. --- Maxima and minima. --- Extremal problems (Mathematics). --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 681.3*F22 Nonnumerical algorithms and problems: complexity of proof procedures; computations on discrete structures; geometrical problems and computations; pattern matching --See also {?681.3*E2-5}; {681.3*G2}; {?681.3*H2-3} --- 519.85 Mathematical programming --- Optimisation mathématique --- Problèmes extrémaux (Mathématiques) --- ELSEVIER-B EPUB-LIV-FT