Variational Methods in Mathematical Physics

Eine gut strukturierte Einführung in die direkte Variationsrechnung aufbauend auf dem Studium kritischer Punkte nichtlinearer Funktionale für Studenten der Mathematik und Physik. Neben Anwendungen auf die Mechanik und die klassische Feldtheorie sowie Rand- und Eigenwertprobleme wichtiger Differentialgleichungen findet man auch die Behandlung der Thomas-Fermi-Theorie.

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This textbook is a comprehensive introduction to variational methods. Its unifying aspect, based on appropriate concepts of compactness, is the study of critical points of functionals via direct methods. It shows the interactions between linear and nonlinear functional analysis. Addressing in particular the interests of physicists, the authors treat in detail the variational problems of mechanics and classical field theories, writing on local linear and nonlinear boundary and eigenvalue problems of important classes of nonlinear partial differential equations, and giving more recent results on Thomas-Fermi theory and on problems involving critical nonlinearities. This book is an excellent introduction for students in mathematics and mathematical physics.