3 problems

Let $n\ge 2$, $1<p<2$, and let $\alpha_{\rm loc}(n,p)>0$ be an admissible interior Hölder exponent for gradients of local $p$-harmonic functions. Is it true that, for every…

Let $\Omega\subset\mathbb{R}^N$, with $1\leq N\leq 3$, be a bounded domain with smooth boundary, and let $u_0\in H^2\cap H_0^1(\Omega)$. Let $\lambda^{*}$ be the critical parameter…

Let $\Omega\subset\mathbb{R}^N$, with $1\leq N\leq 3$, be a bounded domain with smooth boundary, and let $u_0\in H^2\cap H_0^1(\Omega)$. Consider equation (1.1), its solution…