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Estimates on the generalized Morrey spaces \(L_ \varphi^{2,\lambda}\) and BMO\(_ \psi\) for linear elliptic systems. (English) Zbl 0863.35023
We show the regularity in the generalized Morrey spaces \(L^{2,\lambda}_\phi\) and \(\text{BMO}_\psi\) of the gradients of weak solutions to the following elliptic system: \[ -D_\alpha(a^{\alpha\beta}_{ij}D_\beta u^j)=g_i-\text{div }f^i. \] We also investigate \(L^{2,n-2}_\psi\) regularity for gradients of weak solutions of general elliptic systems in divergence form with lower terms where the coefficients satisfy very general conditions. Finally, an a priori estimate in \(\text{BMO}_\psi\) for second-order derivatives of strong solutions of general elliptic systems in nondivergence form is established. The \(\text{BMO}_\psi\) estimate fills in the gap between \(L^p\) estimates and Schauder estimates.

MSC:
35B65 Smoothness and regularity of solutions to PDEs
35J45 Systems of elliptic equations, general (MSC2000)
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