A co-publication of the AMS and Centre de Recherches Mathématiques In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy–Sobolev and Besov spaces. The authors use the so-called “first order approach” which uses minimal assumptions on the coefficients and thus allows for complex coefficients and for systems of equations. This self-contained exposition of the first order approach offers new results with detailed proofs in a clear and accessible way and will become a valuable reference for graduate students and researchers working in partial differential equations and harmonic analysis.
This text offers a clear and concise writing style that is student oriented, combining thorough explanations, an accurate mathematical presentation, and well defined terms.
The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds.
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, ...
(3-2) V “U: lijui—l,j+bijui,j—l+rijui+l,j+tijui,j+l dijuij+€ijr di'j = li'j = ' ' ', 6 ... (Approximating normal derivatives is harder, by all methods!) For example, one can let this H This is the approximation used by Shortley-Weller ...
Suppose there does exist a finite set of vectors {ps : s = 1,2,..., m} in Lee, each of which depends non-trivially on (at most) k of the summands {S, re N}, and such there is a linear combination *n. X_3.p. with 3s € C for s = 1, ...
Coverage includes Fourier series, orthogonal functions, boundary value problems, Green's functions, and transform methods. This text is ideal for readers interested in science, engineering, and applied mathematics.
Normal 0 false false false This book emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations.
KEY BENEFIT Emphasizing physical interpretations of mathematical solutions, this book introduces applied mathematics and presents partial differential equations.
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, ...
This book was written with the student's understanding firmly in mind. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.