This book presents a comprehensive study of boundary value problems for linear and semilinear second order elliptic equations with measure data, especially semilinear 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.

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This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominent lower order reaction term. Emphasis is put on three aspects: