Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Ihsan Topaloglu"'
Publikováno v:
Nonlinear Analysis, 205, pp. 1-19
Nonlinear Analysis, 205, 1-19
Nonlinear Analysis, 205, 1-19
We consider the minimization of an energy functional given by the sum of a crystalline perimeter and a nonlocal interaction of Riesz type, under volume constraint. We show that, in the small mass regime, if the Wulff shape of the anisotropic perimete
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e04392517a90428237eb650265d9af50
https://doi.org/10.1016/j.na.2020.112223
https://doi.org/10.1016/j.na.2020.112223
Autor:
Ihsan Topaloglu, Katy Craig
Publikováno v:
Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 37:239-279
Inspired by recent work on minimizers and gradient flows of constrained interaction energies, we prove that these energies arise as the slow diffusion limit of well-known aggregation-diffusion energies. We show that minimizers of aggregation-diffusio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e24702963afb361d251068d5adefcc2e
https://doi.org/10.1016/j.anihpc.2019.10.003
https://doi.org/10.1016/j.anihpc.2019.10.003
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7493e7237f1a32d15840dc8e3af0a303
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::540cc49bd622c18bd1d5e5bc0884bec5
Publikováno v:
The Journal of Geometric Analysis, 32, 1-31
The Journal of Geometric Analysis, 32, 2, pp. 1-31
The Journal of Geometric Analysis, 32, 2, pp. 1-31
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c2895da63e2ad9c9c07c5bbb2953e2c7
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4a23547c13715f06ac7618acea4d7243
https://hal.archives-ouvertes.fr/hal-02899237
https://hal.archives-ouvertes.fr/hal-02899237
Publikováno v:
Indiana University Mathematics Journal. 67:375-395
We consider a class of nonlocal shape optimization problems for sets of fixed mass where the energy functional is given by an attractive/repulsive interaction potential in power-law form. We find that the existence of minimizers of this shape optimiz
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c7ec10dc2f3bbf557ee988f8024c4e70
https://doi.org/10.1512/iumj.2018.67.6234
https://doi.org/10.1512/iumj.2018.67.6234
We study the singular perturbation of an elastic energy with a singular weight. The minimization of this energy results in a multi-scale pattern formation. We derive an energy scaling law in terms of the perturbation parameter and prove that, althoug
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e932bb22afe0e1d068fc899be8596909
Autor:
Oleksandr Misiats, Ihsan Topaloglu
We consider a variant of Gamow's liquid drop model with an anisotropic surface energy. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface energy is isot
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::05382b4cbe4a5dde928f0901e506e992
We introduce and study certain variants of Gamow's liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are established, the shape of minimizers is analyzed. Under suitable regulari
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a76f9e87de29e352ffdbf2ad66abcad4
http://arxiv.org/abs/1810.08304
http://arxiv.org/abs/1810.08304