Gradient estimates for weak solutions of linear elliptic systems with singular-degenerate coefficients
Dat Cao, Tadele Mengesha, Tuoc V. Phan · Contemporary mathematics - American Mathematical Society · 2019
This paper establishes Calderón-Zygmund type regularity estimates for solutions of the conormal derivative problem for a class of linear elliptic systems in divergence-form with singular, degenerate coefficients in bounded domains. In our class of equations, the principal terms are fourth order tensors of measurable functions that behave as some weight function in the Muckenhoupt class of A 2 A_2 -weights. Regularity estimates for gradient of weak solutions in weighted Lebesgue spaces are established under some natural smallness conditions on the mean oscillation of coefficients. The results obtained recover known results when the coefficients are uniformly elliptic. These results can be considered as the Sobolev counterparts of the classical Hölder’s regularity estimates established by B. Fabes, C. E. Kenig, and R. P. Serapioni.