All Questions

Let $\Omega$ be a bounded domain in $\Bbb R^n$. Define $$ \Omega_r=\{x\in\Omega: \text{dist}(x,\partial\Omega)<r \}, $$ i.e. it the ring of thickness $r$ at the boundary of $\Omega$. Intuitively, ...

In the paper http://cvgmt.sns.it/paper/436/, the author proves the renormalization property for the flow generated by a vector field $a(t,\cdot) \in BV(\mathbb{R}^N; \mathbb{R}^N)$. Heuristically, ...

It is well know that there is a generalization of Lebesgue decomposition theorem in the following way: Any non negative Radon measure can be decomposed uniquely into the sum of an absolutely ...

By Alberti rank-one theorem, could it be possible to reduce the study of a function $u \in BV(\mathbb{R}^N, \mathbb{R}^N)$ to the study of a function $\tilde{u} \in BV(\mathbb{R}^2, \mathbb{R}^2)$? At ...

Let $(\phi_k,\lambda_k)$ be the couple of eigenfunctions and eigenvalues of the the Laplacian operator on $\Omega \subset \mathbb R^n$. The nodal set of $\phi_k$ is the set $$\mathcal N_k = \{x \in \...