By David E Edmunds,Jan Lang,Osvaldo Méndez,Osvaldo Mendez
The thought of Lebesgue and Sobolev areas with variable integrability is experiencing a gentle growth, and is the topic of a lot full of life learn via sensible analysts, function-space analysts and experts in nonlinear research. those areas have attracted recognition not just due to their intrinsic mathematical value as normal, attention-grabbing examples of non-rearrangement-invariant functionality areas but additionally in view in their purposes, which come with the mathematical modeling of electrorheological fluids and snapshot restoration.
The major concentration of this ebook is to supply an exceptional functional-analytic historical past for the learn of differential operators on areas with variable integrability. It contains a few novel balance phenomena which the authors have lately discovered.
At the current time, this is often the single e-book which focuses systematically on differential operators on areas with variable integrability. The authors current a concise, normal advent to the elemental fabric and progressively circulation towards differential operators on those areas, top the reader quick to present study topics.
Contents:
- Preliminaries:
- The Geometry of Banach Spaces
- Spaces with Variable Exponent
- Sobolev areas with Variable Exponent:
- Definition and Functional-analytic Properties
- Sobolev Embeddings
- Compact Embeddings
- Riesz Potentials
- Poincaré-type Inequalities
- Embeddings
- H?lder areas with Variable Exponents
- Compact Embeddings Revisited
- The p(·)-Laplacian:
- Preliminaries
- The p(·)-Laplacian
- Stability with admire to Integrability
- Eigenvalues:
- The by-product of the Modular
- Compactness and Eigenvalues
- Modular Eigenvalues
- Stability with admire to the Exponent
- Convergence houses of the Eigenfunctions
- Approximation on Lp Spaces:
- s-numbers and n-widths
- A Sobolev Embedding
- Integral Operators
Readership: Graduates and researchers drawn to differential operators and serve as spaces.
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Differential Operators on Spaces of Variable Integrability by David E Edmunds,Jan Lang,Osvaldo Méndez,Osvaldo Mendez
by William
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