Given a vector homogeneous differential operator of order 1 A(D) acting on vector fields, I will answer to the question whether there is a Gagliardo--Nirenberg type estimate of the form ||u||_{L^{n/(n...
In this talk we shall present some qualitative results for solutions of the fully nonlinear elliptic Allen Cahn Equation; precisely we shall see that under specific conditions the solutions are one-di...
Dopo aver rivisto alcuni risultati di base e alcuni problemi aperti sul problema isoperimetrico nello spazio Euclideo con densità, discuteremo il caso modello di densità di tipo misto Euclideo-Gaussia...
We prove that any positive solution of \partial_t u-\Delta u+u^q=0 (q>1) in R^N \times (0,\infty) with singular initial trace (F,0), where F is a closed subset of R^N can be represented, up to two ...
In last years, there has been some effort to get quantitative versions of the most classical spectral inequalities, namely the Faber-Krahn inequality for the first eigenvalue of the Dirichlet Laplacia...
L'equazione di Perona-Malik e' stata introdotta ormai vent'anni or sono nel contesto del trattamento d'immagini. Nella sua versione semplificata in dimensione uno si tratta di un'equazione parabolica ...
Two-fluids interfaces are known to be unstable without surface tension because of the formation of Kelvin-Helmholtz instabilities. In presence of surface tension, local existence results can be proved...
Verranno discussi alcuni problemi di frontiera libera della magneto-idrodinamica ideale, dove si trascurano gli effetti di dissipazione o la tensione superficiale, con l'obiettivo più generale di most...
In the paper we give an overview on variational regularization methods in Banach spaces. The theory is developed based on the classical theory of regularization methods in Hilbert spaces. An essential...
The challenges of controlling multiple agent dynamic systems with multiple objectives are related to and furthermore include problems in multi-player dynamic games, multiobjective optimization, and de...
I will briefly discuss the separate computational challenges posed by anisotropy & inhomogeneity in front propagation and optimal control problems. The idea of "homogenization" will be introduced ...
We develop an approach to the construction of Lyapunov functions for the forward equation of a finite-state nonlinear Markov process. Nonlinear Markov processes can be obtained as a law of large numbe...
