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# 📙 Sobolev spaces: with applications to elliptic partial differential equations by Vladimir Maz'ya (auth.) — free download

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Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume ﬁrst appeared in German as three booklets of Teubner-Texte zur Mathematik (1979,1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a signiﬁcantly augmented list of references aim to create a broader and modern view of the area.

- Series:
**Grundlehren der mathematischen Wissenschaften 342** - Author:
**Vladimir Maz'ya (auth.)** - Year:
**2011** - Publisher:
**Springer-Verlag Berlin Heidelberg** - Language:
**English** - ISBN:
**3642155634,9783642155635**

- File size:
**4 831 113** - Format:
**pdf**

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Fourier Series in Several Variables with Applications to Partial Differential Equations illustrates the value of Fourier series methods in solving difficult nonlinear partial differential equations (PDEs). Using these methods, the author presents results ...

Fourier Series in Several Variables with Applications to Partial Differential Equations illustrates the value of Fourier series methods in solving difficult nonlinear partial differential equations (PDEs). Using these methods, the author presents results ...

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesse...

This book brings together ten papers presented at the Conference on Harmonic Analysis and Partial Differential Equations, held in April 1988 at Florida Atlantic University. The papers illuminate the relationship between harmonic analysis and partial diffe...

The book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as m...

Wavelet methods are by now a well-known tool in image processing (jpeg2000). These functions have been used successfully in other areas, however. Elliptic Partial Differential Equations which model several processes in, for example, science and engineeri...

Wavelet methods are by now a well-known tool in image processing (jpeg2000). These functions have been used successfully in other areas, however. Elliptic Partial Differential Equations which model several processes in, for example, science and engineeri...

Wavelet methods are by now a well-known tool in image processing (jpeg2000). These functions have been used successfully in other areas, however. Elliptic Partial Differential Equations which model several processes in, for example, science and engineeri...

Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfac...

<p>The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the m...