On improved regularity of weak solutions of some degenerate,Anisotropic elliptic systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On improved regularity of weak solutions of some degenerate,Anisotropic elliptic systems

Authors:	Tilak Bhattacharya Francesco Leonetti

Institution:	(1) Present address: Indian Statistical Institute, 7SJS Sansanwal Marg, 110 016 New Delhi, India;(2) Present address: Dipartimento di Matematica, Università di L'Aquila, 67100 L'Aquila, Italy

Abstract:	Summary We consider a (possibly) vector-valued function u: R^N, Rⁿ, minimizing the integral $\int\limits_\Omega {(\left\| {D_1 u} \right\|^2 + \ldots + \left\| {D_{n - 1} } \right\|^2 + \left\| {D_n u} \right\|^p )dx}$ , 2-2/(n*1)<p<2, whereD _i u=u/x _i or some more general functional retaining the same behaviour, we prove higher integrability for Du: D₁ u,..., D_n–1 u L^p/(p-1) and D_nu L²; this result allows us to get existence of second weak derivatives: D(D₁ u),...,D(D_n–1u)L² and D(D_n u) L _p.This work has been supported by MURST and GNAFA-CNR.

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