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Full Description
The goal of this book is to investigate the behavior of weak solutions to the elliptic interface problem in a neighborhood of boundary singularities: angular and conic points or edges. This problem is considered both for linear and quasi-linear equations, which are among the less studied varieties. As a second edition of Transmission Problems for Elliptic Second-Order Equations for Non-Smooth Domains (Birkhäuser, 2010), this volume includes two entirely new chapters: one about the oblique derivative problems for the perturbed p(x)-Laplacian equation in a bounded n-dimensional cone, and another about the existence of bounded weak solutions.
Researchers and advanced graduate students will appreciate this compact compilation of new material in the field.
Contents
- 1. Preliminaries.- 2. Eigenvalue Problem and Integro-Differential Inequalities.- 3. Best Possible Estimates of Solutions to the Interface Problem for Linear Elliptic Divergence
Second Order Equations in a Conical Domain.- 4. Interface Problem for the Laplace Operator with N Different Media.- 5. Interface Problem for Weak Quasi-Linear Elliptic Equations in a Conical Domain.- 6. Interface Problem for Strong Quasi-Linear Elliptic Equations in a Conical Domain.- 7. Best Possible Estimates of Solutions to the Interface Problem for a Quasi-Linear Elliptic Divergence Second Order Equation in a Domain with a Boundary Edge.- 8. Interface Oblique Derivative Problem for Perturbed p(x)-Laplacian Equation in a Bounded n- Dimensional Cone.- 9. Existence of Bounded Weak Solutions.
