Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Audrito, Alessandro"'
In this paper, we complete the analysis initiated in [AFV24] establishing some higher order $C^{k+2,\alpha}$ Schauder estimates ($k \in \mathbb{N}$) for a a class of parabolic equations with weights that are degenerate/singular on a characteristic hy
Externí odkaz:
http://arxiv.org/abs/2403.08575
Publikováno v:
Calc. Var. Partial Differential Equations 63-8 (2024), 1-46
We establish some $C^{0,\alpha}$ and $C^{1,\alpha}$ regularity estimates for a class of weighted parabolic problems in divergence form. The main novelty is that the weights may vanish or explode on a characteristic hyperplane $\Sigma$ as a power $a >
Externí odkaz:
http://arxiv.org/abs/2401.06038
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and then we pass
Externí odkaz:
http://arxiv.org/abs/2303.03434
Autor:
Audrito, Alessandro, Kukuljan, Teo
We study the free boundary of solutions to the parabolic obstacle problem with fully nonlinear diffusion. We show that the free boundary splits into a regular and a singular part: near regular points the free boundary is $C^\infty$ in space and time.
Externí odkaz:
http://arxiv.org/abs/2208.14791
Given a bounded domain $D \subset \mathbb{R}^N$ and $m > 1$, we study the long-time behaviour of solutions to the Porous Medium equation (PME) posed in a tube \[ \partial_tu = \Delta u^m \quad \text{ in } D \times \mathbb{R}, \quad t > 0, \] with hom
Externí odkaz:
http://arxiv.org/abs/2204.08224
Autor:
Audrito, Alessandro, Serra, Joaquim
We study critical points of a one-parameter family of functionals arising in combustion models. The problems we consider converge, for infinitesimal values of the parameter, to Bernoulli's free boundary problem, also known as one-phase problem. We pr
Externí odkaz:
http://arxiv.org/abs/2110.09210
Autor:
Audrito, Alessandro
We prove uniform parabolic H\"older estimates of De Giorgi-Nash-Moser type for sequences of minimizers of the functionals \[ \mathcal{E}_\varepsilon(W) = \int_0^\infty \frac{e^{- t/\varepsilon}}{\varepsilon} \bigg\{ \int_{\mathbb{R}_+^{N+1}} y^a \lef
Externí odkaz:
http://arxiv.org/abs/2107.03308
We study the regularity up to the boundary of solutions to the Neumann problem for the fractional Laplacian. We prove that if $u$ is a weak solution of $(-\Delta)^s u=f$ in $\Omega$, $\mathcal N_s u=0$ in $\Omega^c$, then $u$ is $C^\alpha$ up tp the
Externí odkaz:
http://arxiv.org/abs/2006.10026
We study the existence of segregated solutions to a class of reaction-diffusion systems with strong interactions, arising in many physical applications. These special solutions are obtained as weak limits of minimizers of a family of perturbed functi
Externí odkaz:
http://arxiv.org/abs/2004.13638
Autor:
Audrito, Alessandro, Kukuljan, Teo
Publikováno v:
In Journal of Functional Analysis 15 November 2023 285(10)
