Nonlinear Second Order Elliptic Equations Involving Measures

• Main Authors: Marcus, Moshe, Véron, Laurent
• Format: eBook Book
• Language: English
• Published: Germany De Gruyter 2013; Walter de Gruyter GmbH
• Edition: 1
• Series: De Gruyter Series in Nonlinear Analysis and Applications
• Subjects: Analysis of PDEs; Boundary trace; Differential equations, Elliptic; Differential equations, Nonlinear; Elliptic equations; Elliptische Gleichungen; Large solutions; MATHEMATICS; MATHEMATICS / Functional Analysis; MATHEMATICS / Mathematical Analysis; MATHEMATICS / Vector Analysis; Mathematics. Analysis; MATHEMATICS / Differential Equations / General; Maßtheorie; Nichtlineare Analysis; Singularities; Subcritical nonlinearity; Large solutions; Boundary trace; Singularities; Elliptic equations; Elliptische Gleichungen; Subcritical nonlinearity; Nichtlineare Analysis; Maßtheorie; Linear elliptic operators; measures; large solutions; singularities; Green and Poisson potentials; Bessel capacities; boundary traces
• ISBN: 3110305313; 9783110305319; 3110305151; 9783110305159
• DOI: 10.1515/9783110305319

In the last 40 years semi-linear elliptic equations became a central subject of study in the theory of nonlinear partial differential equations. On the one hand, the interest in this area is of a theoretical nature, due to its deep relations to other branches of mathematics, especially linear and nonlinear harmonic analysis, dynamical systems, differential geometry and probability. On the other hand, this study is of interest because of its applications. Equations of this type come up in various areas such as problems of physics and astrophysics, curvature problems in Riemannian geometry, logistic problems related for instance to population models and, most importantly, the study of branching processes and superdiffusions in the theory of probability. The aim of this book is to present a comprehensive study of boundary value problems for linear and semi-linear second order elliptic equations with measure data. We are particularly interested in semi-linear equations with absorption. The interactions between the diffusion operator and the absorption term give rise to a large class of nonlinear phenomena in the study of which singularities and boundary trace play a central role. This book is accessible to graduate students and researchers with a background in real analysis and partial differential equations.