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orthogonal projector onto the set of convex functions

Let $\Omega\subset \mathbb R^d$ be an open, convex domain, and consider the Hilbert space $L^2(\Omega)$. Each sum of convex functions is convex, hence the subset $Conv(\Omega)$ of all convex functions ...
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trace-class embeddings

There is a classical theorem of Riesz-Kolmogorov that characterizes compact embedding in $L^p$-spaces of some subspace of them. A generalization to arbitrary metric spaces has been recently obtained ...
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Let $D_1,D_2$ be a bounded subset of $\mathbb{R}^n$ and $\partial D_1,\partial D_2$ are both of Lebesgue measure zero (that is to say: $D_1,D_2$ are Jordan measurable). Also, let $f:D_1\cup D_2=D\... 0answers 90 views Convergence of solutions of the volterra integral equation with convergent kernels Consider the following Volterra integral equation $$g(t) = \int_0^t K_n(t,s)w_n(s) ds$$ where g(t) and K_n(t,s) are continuous and$K_n(t,s)\geq K_{n+1}(t,s)$for all$t,s$. Moreover,$K_n(t,s)$... 0answers 96 views On the proof of a$W^{2,p}$estimate - regularity on eliptic PDE I see this proof on http://www.math.uiowa.edu/~lwang/cccalderon.pdf and I couldn't understand what he did. If$||f||_{L^p(B_{4})} = \delta$is small and the measure$|\{ x \in B_1; M(|D^2u|^2)>N_1^...
Specificaly: Does convergence in $L^{\frac{1}{2}}$ imply weak $L^2$ convergence? Having a limit in $L^{\frac{1}{2}}$ topology and a limit in weak $L^2$ topology whether these are always equal? If ...