For G open bounded subset of R^2 with C^1 boundary, we study the regularity of the variational solution u in H^1_0(G) to the quasilinear elliptic equation of Leray-Lions type: -div A(x,Du)=f , when f belongs to the Zygmund space L(log L)^{\delta}, \delta>0. As an interpolation between known results for \delta=1/2 and \delta=1 of [Stampacchia] and [Alberico-Ferone], we prove that |Du| belongs to the Lorentz space L^{2, 1/\delta}(G) for \delta in [1/2, 1].
Planar quasilinear elliptic equations with right-hand side in L(log L)^\delta
Alberico A;
2011
Abstract
For G open bounded subset of R^2 with C^1 boundary, we study the regularity of the variational solution u in H^1_0(G) to the quasilinear elliptic equation of Leray-Lions type: -div A(x,Du)=f , when f belongs to the Zygmund space L(log L)^{\delta}, \delta>0. As an interpolation between known results for \delta=1/2 and \delta=1 of [Stampacchia] and [Alberico-Ferone], we prove that |Du| belongs to the Lorentz space L^{2, 1/\delta}(G) for \delta in [1/2, 1].File in questo prodotto:
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