- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type.
The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear elliptic equations as well as their applications to various processes arising in the applied sciences.
The analysis developed in the book is based on the notion of a generalized or weak solution. This approach leads not only to the fundamental results of existence and multiplicity of weak solutions but also to several qualitative properties, including spectral analysis, bifurcation, and asymptotic analysis.
The book examines the equations from different points of view while using the calculus of variations as the unifying theme. Readers will see how all of these diverse topics are connected to other important parts of mathematics, including topology, differential geometry, mathematical physics, and potential theory.
Contents
Isotropic and Anisotropic Function Spaces: Lebesgue and Sobolev Spaces with Variable Exponent. Variational Analysis of Problems with Variable Exponents: Nonlinear Degenerate Problems in Non-Newtonian Fluids. Spectral Theory for Differential Operators with Variable Exponent. Nonlinear Problems in Orlicz-Sobolev Spaces. Anisotropic Problems: Continuous and Discrete: Anisotropic Problems. Difference Equations with Variable Exponent. Appendices. Bibliography. Index.
