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I have this situation: supposing that $\Omega$, is an open, bounded subset of $\mathbb{R}^N$, $N>2$. Given $t_0>0$ and $\overline{n}>0$, let's consider $\overline{t}=t_0+1$, $m>\overline{t}...

It is well known that for any smooth domain $\Omega\subset\mathbb{R}^N$ the energy functional (the one for which the Euler-Lagrange equation is our b.v.p.) associated to the following local problem: $$...