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(Ω)», a class neither containing, nor contained in\(C^0 \left( {\bar \Omega } \right)\). We also prove local and global Lp regularity: this result neither implies, nor follows by the classical one by Agmon, Douglis and Nirenberg.
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Work partially supported by M.P.I.Project 40% «Equazioni di evoluzione e applicazioni fisico-matematiche».
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Acquistapace, P. OnBMO regularity for linear elliptic systems. Annali di Matematica 161, 231–269 (1992). https://doi.org/10.1007/BF01759640
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DOI: https://doi.org/10.1007/BF01759640