Nonlinear Calderón–Zygmund Theory in the Limiting Case

Benny Avelin, Tuomo Kuusi, Giuseppe Mingione*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

39 Citations (Scopus)

Abstract

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 Calderón 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 (Formula presented.) being a Borel measure with locally finite mass on the open subset Ω ⊂ Rn and p> 2 - 1 / n, then (Formula presented.) for every σ ∈ (0,1).The case σ= 1 is obviously forbidden already in the classical linear case of the Poisson equation - ▵u= μ.

Original languageEnglish
Pages (from-to)663-714
Number of pages52
JournalArchive for Rational Mechanics and Analysis
Volume227
Issue number2
DOIs
Publication statusPublished - 1 Feb 2018
MoE publication typeA1 Journal article-refereed

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