Zobrazeno 1 - 10
of 88
pro vyhledávání: '"TOPALOGLU, IHSAN"'
Recently it has been shown that the unique locally perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens partition. Here we
Externí odkaz:
http://arxiv.org/abs/2407.21677
Regular polygons are characterized as area-constrained critical points of the perimeter functional with respect to particular families of perturbations in the class of polygons with a fixed number of sides. We also review recent results in the litera
Externí odkaz:
http://arxiv.org/abs/2406.18163
We characterize the maximizers of a functional that involves the minimization of the Wasserstein distance between sets of equal volume. We prove that balls are the only maximizers by combining a symmetrization-by-reflection technique with the uniquen
Externí odkaz:
http://arxiv.org/abs/2309.05522
We consider a non-local interaction energy over bounded densities of fixed mass $m$. We prove that under certain regularity assumptions on the interaction kernel these energies admit minimizers given by characteristic functions of sets when $m$ is su
Externí odkaz:
http://arxiv.org/abs/2307.01830
We consider a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. It has recently been proved by R. Frank and E. Lieb that the ball is the unique (up to t
Externí odkaz:
http://arxiv.org/abs/2207.00388
We prove the existence of global minimizers to the double minimization problem \[ \inf\Big\{ P(E) + \lambda W_p(\mathcal{L}^n \lfloor \, E,\mathcal{L}^n \lfloor\, F) \colon |E \cap F| = 0, \, |E| = |F| = 1\Big\}, \] where $P(E)$ denotes the perimeter
Externí odkaz:
http://arxiv.org/abs/2108.04390
In this paper we consider a stochastic Keller-Segel type equation, perturbed with random noise. We establish that for special types of random pertubations (i.e. in a divergence form), the equation has a global weak solution for small initial data. Fu
Externí odkaz:
http://arxiv.org/abs/2107.12419
We consider Riesz-type nonlocal interaction energies over polygons. We prove the analog of the Riesz inequality in this discrete setting for triangles and quadrilaterals, and obtain that among all $N$-gons with fixed area, the nonlocal energy is maxi
Externí odkaz:
http://arxiv.org/abs/2103.06657
Autor:
Artac, Inanc, Ilis, Dogan, Karakayali, Muammer, Omar, Timor, Arslan, Ayca, Topaloğlu, Ihsan, Karabag, Yavuz, Karakayon, Suleyman, Rencuzogullari, Ibrahim
Publikováno v:
In The American Journal of the Medical Sciences July 2024
We consider the minimization of an energy functional given by the sum of a density perimeter and a nonlocal interaction of Riesz type with exponent $\alpha$, under volume constraint, where the strength of the nonlocal interaction is controlled by a p
Externí odkaz:
http://arxiv.org/abs/2006.16278