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Weak minima and quasiminima of variational integrals. (English) Zbl 0890.49003
The author proves that there exists $$r_1\in(\max\{1, p-1\},p)$$ such that each very weak solution of the equation $-\text{div}(|\nabla u|^{p- 2}\nabla u)= 0,$ $$u\in W^{1,r}_{\text{loc}}(\Omega)$$, $$r_1< r<p$$, is a $$Q$$-quasiminimum of the functional $$\int_\Omega |Du|^r dx$$ with $$Q$$ independent of $$r$$.
Reviewer: R.Schianchi (Roma)

##### MSC:
 49J40 Variational inequalities
##### Keywords:
quasiminima; very weak solution