An Interior Regularity Property for the Solution to a Linear Elliptic System with Singular Coefficients in the Lower-Order Term

Teresa Radice ()
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Teresa Radice: Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Complesso Universitario Monte S. Angelo, Via Cintia Edificio T, 80126 Napoli, Italy

Mathematics, 2025, vol. 13, issue 3, 1-15

Abstract: This paper deals with the interior higher differentiability of the solution u to the Dirichlet problem related to system − div ( A ( x ) D u ) + B ( x , u ) = f on a bounded Lipschitz domain Ω in R n . The matrix A ( x ) lies in the John and Nirenberg space B M O . The lower-order term B ( x , u ) is controlled with respect to the spatial variable by a function b ( x ) belonging to the Marcinkiewicz space L n , ∞ . The novelty here is the presence of a singular coefficient in the lower-order term.

Keywords: linear elliptic system; BMO space; Hodge decomposition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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