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Zbl 0802.35015
Acquistapace, Paolo
On $BMO$ regularity for linear elliptic systems. (English)
[J] Ann. Mat. Pura Appl., IV. Ser. 161, 231-269 (1992). ISSN 0373-3114; ISSN 1618-1891/e

Summary: We prove a refinement of Campanato's result on local and global (under Dirichlet boundary conditions) BMO regularity for the gradient of solutions of linear elliptic systems of second order in divergence form: we just need that the coefficients are ``small multipliers of $BMO (\Omega)$'', a class neither containing, nor contained in $C\sp 0 (\overline \Omega)$. We also prove local and global $L\sp p$ regularity: this result neither implies, nor follows by the classical one by Agmon, Douglis and Nirenberg.

MSC 2000:: *35D10 Regularity of generalized solutions of PDE
35J45 Systems of elliptic equations, general
46E30 Spaces of measurable functions
46E35 Sobolev spaces and generalizations

Keywords: BMO regularity for the gradient

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