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pro vyhledávání: '"Valette, Anna"'
Autor:
Valette, Anna, Valette, Guillaume
Publikováno v:
Annales Polonici Mathematici vol. 131.1 (2023), 79-84
We establish that if a submanifold $M$ of $\mathbb{R}^n$ is definable in some o-minimal structure then any definable submanifold $N\subset \mathbb{R}^n$ which is $\mathscr{C}^\infty$ diffeomorphic to $M$, with a diffeomorphism $h:N\to M$ that is suff
Externí odkaz:
http://arxiv.org/abs/2403.03164
Publikováno v:
Mathematische Annalen (2024)
We prove that, for any closed semialgebraic subset $W$ of $\mathbb{R}^n$ and for any positive integer $p$, there exists a Nash function $f:\mathbb{R}^n\setminus W\longrightarrow (0, \infty)$ which is equivalent to the distance function from $W$ and a
Externí odkaz:
http://arxiv.org/abs/2403.03135
Autor:
Valette, Anna, Valette, Guillaume
Publikováno v:
Mathematical Inequalities and Applications vol. 26 (2023), 141-150
We first define the trace on a domain $\Omega$ which is definable in an o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$ vanishing on the boundary in the trace sense satisfies Poincar\'e inequality. We finally show, given
Externí odkaz:
http://arxiv.org/abs/2111.05019
Autor:
Valette, Anna, Valette, Guillaume
We prove that if $M\subset \mathbb{R}^n$ is a bounded subanalytic submanifold of $\mathbb{R}^n$ such that $B(x_0,\epsilon)\cap M$ is connected for every $x_0\in\overline{M}$ and $\epsilon>0$ small, then, for $p\in [1,\infty)$ sufficiently large, the
Externí odkaz:
http://arxiv.org/abs/2101.10701
Autor:
Valette, Anna, Valette, Guillaume
Let $\Omega$ be a subanalytic bounded open subset of $\mathbb{R}^n$, with possibly singular boundary. We show that given $p\in [1,\infty)$, there is a constant $C$ such that for any $u\in W^{1,p}(\Omega)$ we have $||u-u_{\Omega}||_{L^p} \le C||\nabla
Externí odkaz:
http://arxiv.org/abs/2010.11529
Autor:
Valette, Anna, Valette, Guillaume
Efroymson's approximation theorem asserts that if $f$ is a $\mathcal{C}^0$ semialgebraic mapping on a $\mathcal{C}^\infty$ semialgebraic submanifold $M$ of $\mathbb{R}^n$ and if $\varepsilon:M\to \mathbb{R}$ is a positive continuous semialgebraic fun
Externí odkaz:
http://arxiv.org/abs/1905.05703
Publikováno v:
In Bulletin des sciences mathématiques July 2023 185
Akademický článek
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Autor:
Valette, Anna, Valette, Guillaume
We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.
Externí odkaz:
http://arxiv.org/abs/1503.04300