In this note we study the global regularity in the Morrey spaces L p,λ for the second derivatives for the strong solutions of non variational elliptic equations.
Key words Extension operator, Lipschitz domains, Sobolev and Morrey spaces MSC (2010) 42B35, 46E30, 46E35We prove that Burenkov's extension operator preserves Sobolev spaces built on general Morrey spaces, including classical Morrey spaces. The analysis concerns bounded and unbounded open sets with Lipschitz boundaries in the n-dimensional Euclidean space.
Interior L p gradient weighted estimates are proved for degenerate elliptic systems in divergence form with VMO coefficients.2010 Mathematics Subject Classification. Primary 35J47.
We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong A ∞ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove C 1,α local estimates for solutions of a degenerate equation in non divergence form.
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