On the generalized Um,pf classes of De Giorgi-Ladyzhenskaya-Ural'tseva and pointwise estimates of solutions to high-order elliptic equations via Wolff potentials

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Skrypnik, Igor I.^1,2  Voitovych, Mykhailo V.¹ 

[1] Natl Acad Sci Ukraine, Inst Appl Math & Mech, Gen Batiouk Str 19, UA-84116 Sloviansk, Ukraine

[2] Vasyl Stus Donetsk Natl Univ, Math Anal & Differential Equat, 600 Richcha Str 21, UA-21021 Vinnytsia, Ukraine

关键词: Quasilinear high-order elliptic equation;    Generalized solution;    Pointwise estimates;    Wolff potential;    Local boundedness;   

DOI  :  10.1016/j.jde.2019.11.051

来源: Elsevier

【 摘 要 】

We consider quasilinear elliptic 2m-order (m >= 2) partial differential equations which prototype is Sigma(vertical bar alpha vertical bar=m) (-1)D-vertical bar alpha vertical bar(alpha)(D(m)u vertical bar(p-2)D(alpha)u) = f(x), x is an element of Omega, where Omega is a bounded open set in R-n, n = mp and f is an element of L (1) (Omega). Using an analogue of the Kilpelainen-Maly method, we obtain the local boundedness and continuity of arbitrary weak solution u is an element of W-m,W-p (Omega) via the Wolff potential W-m,p(f). (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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