Book•
Theory of Orlicz spaces
01 Jan 1991-
TL;DR: A reference/text for mathematicians or students involved in analysis, differential equations, probability theory, and the study of integral operators where only Lebesgue spaces were used in the past is.
Abstract: A reference/text for mathematicians or students involved in analysis, differential equations, probability theory, and the study of integral operators where only Lebesgue spaces were used in the past. Updates and extends the pioneering work by Krasnosel'skii and Rutickii in their 1958 treatise on Orl
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01 Jan 2000
TL;DR: In this article, the Poincare and Sobolev inequalities, pointwise estimates, and pointwise classifications of Soboleve classes are discussed. But they do not cover the necessary conditions for Poincarse inequalities.
Abstract: Introduction What are Poincare and Sobolev inequalities? Poincare inequalities, pointwise estimates, and Sobolev classes Examples and necessary conditions Sobolev type inequalities by means of Riesz potentials Trudinger inequality A version of the Sobolev embedding theorem on spheres Rellich-Kondrachov Sobolev classes in John domains Poincare inequality: examples Carnot-Caratheodory spaces Graphs Applications to PDE and nonlinear potential theory Appendix References.
1,093 citations
Book•
01 May 1996
TL;DR: In this article, a concise treatment of the theory of nonlinear evolutionary partial differential equations is provided, and a rigorous analysis of non-Newtonian fluids is provided for applications in physics, biology, and mechanical engineering.
Abstract: This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering
795 citations
TL;DR: In this article, the authors prove regularity results for weak solutions to systems modelling electro-rheological fluids in the stationary case, as proposed in [27, 31].
Abstract: We prove regularity results for weak solutions to systems modelling electro-rheological fluids in the stationary case, as proposed in [27, 31]; a particular case of the system we consider is
595 citations
TL;DR: In this paper, the integral functional under non-standard growth assumptions was considered and the regularity of minimizers was proved under sharp assumptions on the continuous function p(x) > 1.
Abstract: We consider the integral functional under non-standard growth assumptions that we call p(x) type: namely, we assume that a relevant model case being the functional Under sharp assumptions on the continuous function p(x)>1 we prove regularity of minimizers. Energies exhibiting this growth appear in several models from mathematical physics.
509 citations
Cites methods from "Theory of Orlicz spaces"
...We consider the Orlicz space generated by A, that is the Banach space L( ) (we refer the reader to the classical monograph [27] for a complete account of the theory), equipped with the following Luxemburg norm: ‖h‖A := inf { λ > 0 : − ∫ A ( |h| λ ) dx 1 } ....
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TL;DR: In this article, a multi-sublinear maximal operator that acts on the product of m Lebesgue spaces and is smaller than the m-fold product of the Hardy-Littlewood maximal function is studied.
462 citations
Cites background from "Theory of Orlicz spaces"
...For more information and a lively exposition about these spaces the reader may consult the book by Wilson [50] or [46]....
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