Nonlinear Caldern-Zygmund Theory in the Limiting Case

被引:85
作者
Avelin, Benny [1 ]
Kuusi, Tuomo [2 ]
Mingione, Giuseppe [3 ]
机构
[1] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden
[2] Aalto Univ, Dept Math & Syst Anal, POB 11100, Aalto 00076, Finland
[3] Univ Parma, Dipartimento Matemat & Informat, Parco Area Sci 53-A, I-43124 Parma, Italy
基金
瑞典研究理事会;
关键词
ELLIPTIC-EQUATIONS; PARABOLIC EQUATIONS; LAPLACE EQUATIONS; SINGULAR SET; REGULARITY; FUNCTIONALS; GRADIENT; SYSTEMS; POTENTIALS; GROWTH;
D O I
10.1007/s00205-017-1171-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 .
引用
收藏
页码:663 / 714
页数:52
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