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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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