Zobrazeno 1 - 10
of 145
pro vyhledávání: '"Ponce Augusto C."'
Autor:
Ponce, Augusto C., Spector, Daniel
Publikováno v:
Lenhart, Suzanne and Xiao, Jie. Potentials and Partial Differential Equations: The Legacy of David R. Adams, De Gruyter, 2023
We present results for Choquet integrals with minimal assumptions on the monotone set function through which they are defined. They include the equivalence of sublinearity and strong subadditivity independent of regularity assumptions on the capacity
Externí odkaz:
http://arxiv.org/abs/2302.11847
We prove that each Borel function $V : \Omega \to [-\infty, +\infty]$ defined on an open subset $\Omega \subset \mathbb{R}^{N}$ induces a decomposition $\Omega = S \cup \bigcup_{i} D_{i}$ such that every function in $W^{1,2}_{0}(\Omega) \cap L^{2}(\O
Externí odkaz:
http://arxiv.org/abs/2111.05913
Autor:
Detaille, Antoine, Ponce, Augusto C.
We prove that every finite Borel measure $\mu$ in $\mathbb{R}^N$ that is bounded from above by the Hausdorff measure $\mathcal{H}^s$ can be split in countable many parts $\mu\lfloor_{E_k}$ that are bounded from above by the Hausdorff content $\mathca
Externí odkaz:
http://arxiv.org/abs/2010.15902
Autor:
Ponce, Augusto C., Wilmet, Nicolas
We prove an integral representation formula for the distributional normal derivative of solutions of $$ \left\{ \begin{aligned} - \Delta u + V u &= \mu && \text{in $\Omega$,} u &= 0 && \text{on $\partial\Omega$,} \end{aligned} \right. $$ where $V \in
Externí odkaz:
http://arxiv.org/abs/2009.02977
Publikováno v:
J. London Math. Soc. (2) 106 (2022), 1603-1627
Given a finite nonnegative Borel measure $m$ in $\mathbb{R}^{d}$, we identify the Lebesgue set $\mathcal{L}(V_{s}) \subset \mathbb{R}^{d}$ of the vector-valued function $$V_{s}(x) = \int_{\mathbb{R}^{d}}\frac{x - y}{|x - y|^{s + 1}} \mathrm{d}m(y), $
Externí odkaz:
http://arxiv.org/abs/2006.11046
Autor:
Ponce, Augusto C., Wilmet, Nicolas
We prove the Hopf boundary point lemma for solutions of the Dirichlet problem involving the Schr\"odinger operator $- \Delta + V$ with a nonnegative potential $V$ which merely belongs to $L_{\mathrm{loc}}^1(\Omega)$. More precisely, if $u \in W_0^{1,
Externí odkaz:
http://arxiv.org/abs/2001.03341
We establish that for every function $u \in L^1_\mathrm{loc}(\Omega)$ whose distributional Laplacian $\Delta u$ is a signed Borel measure in an open set $\Omega$ in $\mathbb{R}^{N}$, the distributional gradient $\nabla u$ is differentiable almost eve
Externí odkaz:
http://arxiv.org/abs/1810.03924
Autor:
Orsina, Luigi, Ponce, Augusto C.
Publikováno v:
J. Math. Pures Appl. (2019)
Given any Borel function $V : \Omega \to [0, +\infty]$ on a smooth bounded domain $\Omega \subset \mathbb{R}^{N}$, we establish that the strong maximum principle for the Schr\"odinger operator $-\Delta + V$ in $\Omega$ holds in each Sobolev-connected
Externí odkaz:
http://arxiv.org/abs/1808.07267
Autor:
Ponce, Augusto C., Spector, Daniel
We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space $W^{k,1}(\mathbb{R}^d)$ as the difference of two non-negative functions in the same space with control of their norms.
Externí odkaz:
http://arxiv.org/abs/1807.05221
Autor:
Ponce, Augusto C., Wilmet, Nicolas
Publikováno v:
SIAM J. Control Optim. 56 (2018), no. 4, 2513-2535
We study the minimization of the cost functional \[ F(\mu) = \lVert u - u_d \rVert_{L^p(\Omega)} + \alpha \lVert \mu \rVert_{\mathcal{M}(\Omega)}, \] where the controls $\mu$ are taken in the space of finite Borel measures and $u \in W_0^{1, 1}(\Omeg
Externí odkaz:
http://arxiv.org/abs/1712.06159