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Consider the fractional Laplacian defined by $$(-\Delta)^s u(x) = P.V. \int_{\mathbb{R}^N} \frac{u(x) - u(y)}{|x - y|^{N + 2s}}dy, \ s \in (0,1).$$ Also consider that $$D((-\Delta)^s) = \{u \in H^s(\...

Let $\mu_. : \mathbb{R}^+ \rightarrow M_F(\mathbb{N}) $ a function. We set up : $$ \mu_t = \sum a_i(t) \delta_i$$ where each $a_i$ is a positive continuous function from $\mathbb{R}^+$ to $\mathbb{R}^+...

I'm looking for some references about the theory of regular Lagrangian flows on a smooth domain $\Omega$ of $\mathbb{R}^d$ (say a smooth bounded open set of $\mathbb{R}^d$ or a half space). Here, ...

In Brezis's Functional Analysis book through chapters 3-4, I've seen the $\sigma(L^\infty,L^1)$ topology on $L^\infty$ but did not see (so far) any application of it in differential equations. Is ...