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pro vyhledávání: '"Caffarelli, Luis"'
A horizontal $N$-dimensional plane, having a diffusion of its own, exchanges with the lower half space. There, a reaction-diffusion process, modelled by a free boundary problem, takes place. We wish to understand whether, and how, the free boundary m
Externí odkaz:
http://arxiv.org/abs/2211.15099
The non-local in space two-phase Stefan problem (a prototype in phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admits a unique weak solution. This formulation makes Stefan problem to be
Externí odkaz:
http://arxiv.org/abs/2111.15600
Publikováno v:
Analysis & PDE 17 (2024) 243-279
We introduce a new family of intermediate operators between the fractional Laplacian and the Caffarelli-Silvestre nonlocal Monge-Amp\`ere that are given by infimums of integro-differential operators. Using rearrangement techniques, we obtain represen
Externí odkaz:
http://arxiv.org/abs/2111.12781
Autor:
Caffarelli, Luis, Tomasetti, Ignacio
In this paper we generalize an equation studied by Mossino and Temam, to the fully nonlinear case. This equation arises in plasma physics as an approximation to Grad equations, which were introduced by Harold Grad, to model the behavior of plasma con
Externí odkaz:
http://arxiv.org/abs/2007.05654
We complete the description, initiated in [6], of a free boundary travelling at constant speed in a half plane, where the propagation is controlled by a line having a large diffusion on its own. The main result of this work is that the free boundary
Externí odkaz:
http://arxiv.org/abs/2003.14005
Akademický článek
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On uniqueness of solutions to viscous HJB equations with a subquadratic nonlinearity in the gradient
Publikováno v:
Communications in Partial Differential Equations 44 (2019), no. 12, 1466-1480
Uniqueness of positive solutions to viscous Hamilton-Jacobi-Bellman (HJB) equations of the form $-\Delta u(x) + \frac{1}{\gamma} |D{u}(x)|^\gamma = f(x) - \lambda$, with $f$ a coercive function and $\lambda$ a constant, in the subquadratic case, that
Externí odkaz:
http://arxiv.org/abs/1906.11733