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

Title:

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

Creator:

Lattorusso, Luisa

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:0fa6dda3-5245-4235-a7dc-61223cfa1364
uuid:0fa6dda3-5245-4235-a7dc-61223cfa1364

Subject:

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

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $\Omega$ be a bounded open subset of $\mathbb{R}^{n}$, $n>2$. In $\Omega$ we deduce the global differentiability result \[u \in H^{2}(\Omega, \mathbb{R}^{N}) \] for the solutions $u \in H^{1}(\Omega, \mathbb{R}^{n})$ of the Dirichlet problem \[ u-g \in H^{1}_{0}(\Omega, \mathbb{R}^{N}), -\sum _{i}D_{i}a^{i}(x,u,Du)=B_{0}(x,u,Du) \] 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

113-129

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:1

Harvested from:

CDK

Metadata only:

false