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

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.


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
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