Heriot-Watt Mathematics Report Series
HWM01-4, 1 March 2001
Sufficiency theorems for local minimizers of the multiple integrals of the calculus of variations
A Taheri
Abstract
We establish sufficient conditions on a given Sobolev function $u_0$ to be an $L^r$ local minimizer ($1 \le r \le \infty$) of an integral functional of the type
$$
I(u)= \int_{\Omega} f(x,u,Du) \, dx.
$$
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