On the Higher Integrability of the Gradient of Weak Solutions of Certain Degenerate Elliptic Systems

Higher integrability for parabolic systems with non-standard growth and degenerate diffusions

“…At this stage we point out that a complete Calderón-Zygmund theory for the pLaplacean equation was essentially obtained by Iwaniec [27], while the vectorial case, i.e. the case of systems, was treated by DiBenedetto and Manfredi [18]. For similar results concerning equations with VMO-coefficients we refer to [31], [32] and the references therein.…”

Quasilinear elliptic equations with BMO coefficients in Lipschitz domains

“…This is a classical question, and there have been many works in this direction (see e.g. [4,6,10,11]). In [10,11] the authors considered the Dirichlet problem for (1.1) to prove the well posedness in W 1,q (Ω) under the assumptions that A is 5900 SUN-SIG BYUN AND LIHE WANG of the space VMO and that ∂Ω is locally C 1,α , 0 < α ≤ 1.…”

On the Calderon-Zygmund Theory for Nonlinear Parabolic Problems with Nonstandard Growth Condition

“…The result for the stationary p-Laplacian equation was established in (Iwaniec, 1983), while the result for the p-Laplacian system was proved in (DiBenedetto & Manfredi, 1993). The fact, that for elliptic equations with VMO coefficients, the Calderón-Zygmund estimates for the gradient on L q -level for q > p are valid, was shown in (Kinnunen & Zhou, 1999).…”