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Sobolev (Triebel-Lizorkin) norm estimate for $F \circ u - F \circ v$

Let $F \in C^1(\mathbb R^d;\mathbb R)$ be such that $F(0) = 0$ and $$|F'(\tau v + (1 - \tau)w)| \leq \mu(\tau)(G(v) + G(w))$$ for some $\mu \in L^1([0,1])$ and some non-negative $G \in C^0(\mathbb R^d;...
Desura's user avatar
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Estimatives for elliptic systems involving the laplacian

Considering the problem \begin{equation} \left\{ \begin{array}[c]{11} \Delta(\Delta \chi -\chi) = 0 & \text{in } \Omega, \\ \Delta \chi -\chi = h_2 - h_1, & \text{on } \partial\Omega \\ \end{...
Bruno Mascaro's user avatar