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The Calderón–Zygmund estimates for a class of nonlinear elliptic equations with measure data
Author(s) -
Liang Shuang,
Zheng Shenzhou
Publication year - 2021
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800334
Subject(s) - mathematics , measure (data warehouse) , sobolev space , nonlinear system , class (philosophy) , mathematical analysis , order (exchange) , constant (computer programming) , radon measure , integrable system , pure mathematics , finance , quantum mechanics , database , artificial intelligence , computer science , economics , programming language , locally compact space , physics
We study a class of nonlinear elliptic equations involving measure data− divA ( x , D u ) = μ in Ω , where μ is a Radon measure. Under the main assumption of A ( x , ξ ) that there exists a constant Λ > 0 such that| A ( x , ξ ) − A ( x 0 , ξ ) | ≤ Λ ( a ( x ) + a ( x 0 ) ) | x − x 0 | α( | ξ | 2 + s 2 )p − 1 2 , α ∈ ( 0 , 1 ] , where 0 ≤ a ( x ) ∈ L m ( Ω )for some integrable index m > 1 , we obtain the Calderón–Zygmund estimates in the Sobolev–Morrey spaces for refined fractional‐order derivatives of distributional solutions depending on α.