Existence And Regularity Theory In Weighted Sobolev Spaces And Applications
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Existence and Regularity Theory in Weighted Sobolev Spaces and Applications
Słowa kluczowe: weighted Poincare inequality, weighted Orlicz-Sobolev spaces, weighted Orlicz-Slobodetskii spaces, isoperimetric inequalities, weighted Sobolev spaces, $p$-Laplace equation, Baire Category method, extension operator, nonhomogeneous boundaryvalue problem, trace theorem, degenerate elliptic PDEs, upper and lower bounds of eigenvalues, two weighted Poincare inequality, eigenvalue problems, nonexistence.
Theory and Applications of Viscous Fluid Flows
Author: Radyadour Kh. Zeytounian
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-06-29
This book is the natural sequel to the study of nonviscous fluid flows pre sented in our recent book entitled "Theory and Applications of Nonviscous Fluid Flows" and published in 2002 by the Physics Editorial Department of Springer-Verlag (ISBN 3-540-41412-6 Springer-Verlag, Berlin, Heidelberg, New York). The physical concept of viscosity (for so-called "real fluids") is associated both incompressible and compressible fluids. Consequently, we have with a vast field of theoretical study and applications from which any subsection could have itself provided an area for a single book. It was, however, decided to attempt aglobaI study so that each chapter serves as an introduction to more specialized study, and the book as a whole presents a necessary broad foundation for furt her study in depth. Consequently, this volume contains many more pages than my preceding book devoted to nonviscous fluid flows and a large number (80) of figures. There are three main models for the study of viscous fluid flows: First, the model linked with viscous incompressible fluid flows, the so-called (dynamic) Navier model, governing linearly viscous divergenceless and homogeneous fluid flows. The second is the sü-called Navier-Stokes model (NS) which is linked to compressible, linearly viscous and isentropic equations für a polytropic viscous gas. The third is the so-called Navier-Stokes-Fourier model (NSF) that gov erns the motion of a compressible, linearly viscous, heat-conducting gas.
Weighted Sobolev Spaces and Degenerate Elliptic Equations
Author: Albo Carlos Cavalheiro
language: en
Publisher: Cambridge Scholars Publishing
Release Date: 2023-09-29
In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is disturbed in the sense that some degeneration or singularity appears. This bad behavior can be caused by the coefficients of the corresponding differential operator as well as by the solution itself. There are several very concrete problems in various practices which lead to such differential equations, such as glaciology, non-Newtonian fluid mechanics, flows through porous media, differential geometry, celestial mechanics, climatology, and reaction-diffusion problems, among others. This book is based on research by the author on degenerate elliptic equations. This book will be a useful reference source for graduate students and researchers interested in differential equations.