On the regularity of very weak solutions for linear elliptic equations in divergence form

In this paper we consider a linear elliptic equation in divergence form 0.1 ∑ i , j D j ( a ij ( x ) D i u ) = 0 in Ω . Assuming the coefficients a ij in W 1 , n ( Ω ) with a modulus of continuity satisfying a certain Dini-type continuity condition, we prove that any very weak solution u ∈ L loc n ′...

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Published inNonlinear differential equations and applications Vol. 27; no. 5
Main Authors La Manna, Domenico Angelo, Leone, Chiara, Schiattarella, Roberta
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2020
Springer Nature B.V
Subjects
Analysis
Continuity
Divergence
Elliptic functions
Mathematics
Mathematics and Statistics
Very weak solutions
Elliptic equations
Primary 35-02
Secondary 35B65
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Summary:In this paper we consider a linear elliptic equation in divergence form 0.1 ∑ i , j D j ( a ij ( x ) D i u ) = 0 in Ω . Assuming the coefficients a ij in W 1 , n ( Ω ) with a modulus of continuity satisfying a certain Dini-type continuity condition, we prove that any very weak solution u ∈ L loc n ′ ( Ω ) of ( 0.1 ) is actually a weak solution in W loc 1 , 2 ( Ω ) .
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-020-00646-8