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Nonlinear Caldern-Zygmund Theory in the Limiting Case
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.ORCID iD: 0000-0002-1429-4965
Aalto Univ, Dept Math & Syst Anal, POB 11100, Aalto 00076, Finland..
Univ Parma, Dipartimento Matemat & Informat, Parco Area Sci 53-A, I-43124 Parma, Italy..ORCID iD: 0000-0001-8552-2550
2018 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 227, no 2, p. 663-714Article in journal (Refereed) Published
Abstract [en]

We prove a maximal differentiability and regularity result for solutions to nonlinear measure data problems. Specifically, we deal with the limiting case of the classical theory of Caldern and Zygmund in the setting of nonlinear, possibly degenerate equations and we show a complete linearization effect with respect to the differentiability of solutions. A prototype of the results obtained here tells for instance that ifwith being a Borel measure with locally finite mass on the open subset and , thenThe case is obviously forbidden already in the classical linear case of the Poisson equation.

Place, publisher, year, edition, pages
2018. Vol. 227, no 2, p. 663-714
National Category
Mathematics Mechanical Engineering
Identifiers
URN: urn:nbn:se:uu:diva-341484DOI: 10.1007/s00205-017-1171-7ISI: 000419122300006OAI: oai:DiVA.org:uu-341484DiVA, id: diva2:1186437
Available from: 2018-02-28 Created: 2018-02-28 Last updated: 2018-02-28Bibliographically approved

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Avelin, Benny

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