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pro vyhledávání: '"Villegas, Salvador"'
In the regularity theory of solutions to elliptic partial differential equations often the concept of stability plays the role of a sufficient condition for smoothness. It is a natural question to ask if this holds true for nonstable but finite Morse
Externí odkaz:
http://arxiv.org/abs/2404.06944
Publikováno v:
Journal of Management History, 2023, Vol. 30, Issue 1, pp. 41-59.
Externí odkaz:
http://www.emeraldinsight.com/doi/10.1108/JMH-07-2022-0026
Autor:
Villegas, Salvador
Consider the semilinear elliptic equation $-\Delta u=\lambda f(u)$ in the unit ball $B_1\subset \mathbb{R}^N$, with Dirichlet data $u|_{\partial B_1}=0$, where $\lambda\geq 0$ is a real parameter and $f$ is a $C^1$ positive, nondecreasing and convex
Externí odkaz:
http://arxiv.org/abs/2005.14334
Autor:
Villegas, Salvador
Consider the equation div$(\varphi^2 \nabla \sigma)=0$ in $\mathbb{R}^N,$ where $\varphi>0$. Berestycki, Caffarelli and Nirenberg proved that if there exists $C>0$ such that $\int_{B_R}(\varphi \sigma)^2 \leq CR^2$ for every $R\geq 1$ then $\sigma$ i
Externí odkaz:
http://arxiv.org/abs/2003.09289
Autor:
Villegas, Salvador
Consider the equation div$(\varphi^2 \nabla \sigma)=0$ in $\mathbb{R}^N,$ where $\varphi>0$. It is well-known that if there exists $C>0$ such that $\int_{B_R}(\varphi \sigma)^2 dx\leq CR^2$ for every $R\geq 1$ then $\sigma$ is necessarily constant. I
Externí odkaz:
http://arxiv.org/abs/2003.04400
Publikováno v:
The CASE Journal, 2022, Vol. 18, Issue 6, pp. 913-932.
Externí odkaz:
http://www.emeraldinsight.com/doi/10.1108/TCJ-06-2021-0090
This article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-dimensional case, we introduce the continuous odd rearrangement of an
Externí odkaz:
http://arxiv.org/abs/1709.07656
Publikováno v:
Communications on Pure & Applied Analysis; Mar2025, Vol. 24 Issue 3, p1-7, 7p
Autor:
Villegas, Salvador
Publikováno v:
In Journal of Differential Equations 5 January 2021 270:947-960