Guide to nonlinear potential estimates

One of the basic achievements in nonlinear potential theory is that the typical linear pointwise estimates via fundamental solutions find a precise analog in the case of nonlinear equations. We give a comprehensive account of this fact and prove new unifying families of potential estimates. We also...

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Bibliographic Details
Published inBulletin of mathematical sciences Vol. 4; no. 1; pp. 1 - 82
Main Authors Kuusi, Tuomo, Mingione, Giuseppe
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.01.2014
World Scientific Publishing Co. Pte., Ltd
Springer Basel
Subjects
Mathematics
Mathematics and Statistics
Potential Estimates
Measure Data Problems
Fractional Maximal Operator
Riesz Potential
Wolff Potential
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Summary:One of the basic achievements in nonlinear potential theory is that the typical linear pointwise estimates via fundamental solutions find a precise analog in the case of nonlinear equations. We give a comprehensive account of this fact and prove new unifying families of potential estimates. We also describe new fine properties of solutions to measure data problems.
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Communicated by Neil Trudinger.
ISSN:1664-3607
1664-3615
DOI:10.1007/s13373-013-0048-9