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This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.

Calculus of variations. --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima

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Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.

Mathematical statistics. --- Maxima and minima. --- Mathematical statistics --- Maxima and minima --- Statistique mathématique --- Maxima et minima --- 519.5 --- Academic collection --- Minima --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics

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Numerical methods of optimisation --- Mathematical optimization. --- Optimisation mathématique --- Mathematical optimization --- 519.8 --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Operational research --- 519.8 Operational research --- Optimisation mathématique

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The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a state-of-the-art reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes.

Stochastic processes --- Partial differential equations --- Differential geometry. Global analysis --- Viscosity solutions --- Congresses. --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Congresses --- Partial differential equations. --- Probabilities. --- Calculus of variations. --- Partial Differential Equations. --- Probability Theory and Stochastic Processes. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Viscosity solutions - Congresses.

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Quantum chemistry --- fysicochemie --- Calculus of variations --- 530.145 --- #WSCH:AAS2 --- Chemistry, Quantum --- Chemistry, Physical and theoretical --- Quantum theory --- Excited state chemistry --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Calculus of variations. --- Quantum chemistry. --- Brillouin theorem --- Hartree-fock --- Hylleraas --- Lagrange --- Perturbation --- SCF --- Schrodinger --- UHF --- USCF --- Brillouin theorem. --- Hartree-fock. --- Hylleraas. --- Lagrange. --- Perturbation. --- SCF. --- Schrodinger. --- UHF. --- USCF. --- 530.145 Quantum theory