On \(BMO\) regularity for linear elliptic systems. (English) Zbl 0802.35015

Acquistapace, Paolo

Ann. Mat. Pura Appl., IV. Ser. 161, 231-269 (1992).

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 \(C^ 0 (\overline \Omega)\). We also prove local and global \(L^ p\) regularity: this result neither implies, nor follows by the classical one by Agmon, Douglis and Nirenberg.

MSC:

35D10	Regularity of generalized solutions of PDE (MSC2000)
35J45	Systems of elliptic equations, general (MSC2000)
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

BMO regularity for the gradient

References:

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