ترغب بنشر مسار تعليمي؟ اضغط هنا

On the Lebesgue measure of the boundary of the evoluted set

52   0   0.0 ( 0 )
 نشر من قبل Francesco Rossi
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

The evoluted set is the set of configurations reached from an initial set via a fixed flow for all times in a fixed interval. We find conditions on the initial set and on the flow ensuring that the evoluted set has negligible boundary (i.e. its Lebesgue measure is zero). We also provide several counterexample showing that the hypotheses of our theorem are close to sharp.



قيم البحث

اقرأ أيضاً

We show that the Julia set of the Feigenbaum polynomial has Hausdorff dimension less than~2 (and consequently it has zero Lebesgue measure). This solves a long-standing open question.
In this paper, we are going to discuss the following problem: Let $T$ be a fixed set in $mathbb{R}^n$. And let $S$ and $B$ he two subsets in $mathbb{R}^n$ such that for any $x$ in $S$, there exists an $r$ such that $x+ r T$ is a subset of $B$. How sm all can be $B$ be if we know the size of $S$? Stein proved that for $n$ is greater than or equal to 3 and $T$ is a sphere centered at origin, then $S$ has positive measure implies $B$ has positive measure using spherical maximal operator. Later, Bourgain and Marstrand proved the similar result for $n =2$. And we found an example for why the result fails for $n=1$.
626 - M. Formentin , C. Kuelske 2009
We consider the free boundary condition Gibbs measure of the Potts model on a random tree. We provide an explicit temperature interval below the ferromagnetic transition temperature for which this measure is extremal, improving older bounds of Mossel and Peres. In information theoretic language extremality of the Gibbs measure corresponds to non-reconstructability for symmetric q-ary channels. The bounds are optimal for the Ising model and appear to be close to what we conjecture to be the true values up to a factor of 0.0150 in the case q = 3 and 0.0365 for q = 4. Our proof uses an iteration of random boundary entropies from the outside of the tree to the inside, along with a symmetrization argument.
We investigate Weierstrass functions with roughness parameter $gamma$ that are Holder continuous with coefficient $H={loggamma}/{log frac12}.$ Analytical access is provided by an embedding into a dynamical system related to the baker transform where the graphs of the functions are identified as their global attractors. They possess stable manifolds hosting Sinai-Bowen-Ruelle (SBR) measures. We systematically exploit a telescoping property of associated measures to give an alternative proof of the absolute continuity of the SBR measure for large enough $gamma$ with square-integrable density. Telescoping allows a macroscopic argument using the transversality of the flow related to the mapping describing the stable manifold. The smoothness of the SBR measure can be used to compute the Hausdorff dimension of the graphs of the original Weierstrass functions and investigate their local times.
126 - Jayanta Sarkar 2021
In this article, we are concerned with a certain type of boundary behavior of positive solutions of the heat equation on a stratified Lie group at a given boundary point. We prove that a necessary and sufficient condition for the existence of the par abolic limit of a positive solution $u$ at a point on the boundary is the existence of the strong derivative of the boundary measure of $u$ at that point. Moreover, the parabolic limit and the strong derivative are equal.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا