A global differentiability result for solutions of nonlinear elliptic problems with controlled growths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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A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Authors:

Institution:

(1) DIMET, Facoltà di Ingegneria Universitá “Mediterranea” degli Studi di Reggio Calabria, Via Graziella (Loc. Feo Di Vito), Reggio Calabria, Italy

Abstract:

Let Ω be a bounded open subset of ℝⁿ, n > 2. In Ω we deduce the global differentiability result

$u \in H^2 (\Omega ,\mathbb{R}^N )$

for the solutions u ∈ H ¹ (Ω, ℝⁿ) of the Dirichlet problem

$u - g \in H_0^1 (\Omega ,\mathbb{R}^N ), - \sum\limits_i {D_i a^i (x,u,Du)} = B_0 (x,u,Du)$

with controlled growth and nonlinearity q = 2. The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.

Keywords:

global differentiability of weak solutions elliptic problems controlled growth nonlinearity with q = 2

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