By David E Edmunds,Jan Lang,Osvaldo Méndez,Osvaldo Mendez
The idea of Lebesgue and Sobolev areas with variable integrability is experiencing a gradual enlargement, and is the topic of a lot full of life learn through practical analysts, function-space analysts and experts in nonlinear research. those areas have attracted cognizance not just due to their intrinsic mathematical significance as usual, 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 photo restoration.
The major concentration of this e-book is to supply a great functional-analytic history for the learn of differential operators on areas with variable integrability. It comprises a few novel balance phenomena which the authors have lately discovered.
At the current time, this is often the one booklet which focuses systematically on differential operators on areas with variable integrability. The authors current a concise, typical creation to the fundamental fabric and progressively flow towards differential operators on those areas, prime the reader fast to present learn topics.
- 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
- H?lder areas with Variable Exponents
- Compact Embeddings Revisited
- The p(·)-Laplacian:
- The p(·)-Laplacian
- Stability with recognize to Integrability
- 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 attracted to differential operators and serve as spaces.
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Extra info for Differential Operators on Spaces of Variable Integrability
Differential Operators on Spaces of Variable Integrability by David E Edmunds,Jan Lang,Osvaldo Méndez,Osvaldo Mendez