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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
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