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Theorem 5 p.84 of J. Simons paper "Compact sets in the space $L^p(0,T;B)$" states a generalization of the Aubin-Lions lemma which relaxes the required regularity in time to the existence of a modulus …

I am interested in equations of the form $$(\Delta -|u|^2)f = F(u)$$ where $F$ depends on $u$ and preferably on its derivative, too. $u$ is supposed to be given and $f$ the unknown. More precisely I a …

Let $f\in W^{1,12/5}(\mathbb{R}^3)$ (time-independent), let $K^{\epsilon}$ be a uniformly in $\epsilon$ bounded sequence in $L^{1}\cap L^{7/5}(\mathbb{R}^3)$ and let $$\tilde{K}^{\epsilon} := K^{\epsi …

For reference, I am reading the paper "Uniqueness of Finite Energy Solutions for Maxwell-Dirac and Maxwell-Klein-Gordon Equations" by Masmoudi and Nakanishi. Let $A_0$ be a scalar function satisfying …

Let's say I have an equation of the form $\Delta A = J$ where $J=u\nabla u + A|u|^2$ (Clarification: We are on $\mathbb{R}^3$ and $u$ is assumed to be in $H^1(\mathbb{R}^3)$). Then I could simply infe …