Zobrazeno 1 - 10
of 315
pro vyhledávání: '"Chan, Hardy"'
We propose a possible nonlocal approximation of the Willmore functional, in the sense of Gamma-convergence, based on the first variation ot the fractional Allen-Cahn energies, and we prove the corresponding $\Gamma$-limsup estimate. Our analysis is b
Externí odkaz:
http://arxiv.org/abs/2407.06102
Minimal surfaces in closed 3-manifolds are classically constructed via the Almgren-Pitts approach. The Allen-Cahn approximation has proved to be a powerful alternative, and Chodosh and Mantoulidis (in Ann. Math. 2020) used it to give a new proof of Y
Externí odkaz:
http://arxiv.org/abs/2308.06328
This paper is devoted to describing a linear diffusion problem involving fractional-in-time derivatives and self-adjoint integro-differential space operators posed in bounded domains. One main concern of our paper is to deal with singular boundary da
Externí odkaz:
http://arxiv.org/abs/2304.04431
Autor:
Chan, Hardy
In a bounded domain, we consider a variable range nonlocal operator, which is maximally isotropic in the sense that its radius of interaction equals the distance to the boundary. We establish $C^{1,\alpha}$ boundary regularity and existence results f
Externí odkaz:
http://arxiv.org/abs/2303.07481
Autor:
Chan, Hardy, DelaTorre, Azahara
Point singularities of solutions to the classical Lane-Emden-Serrin equation have a polyhomogeneous asymptotic expansion whose logarithmic corrections are determined by a first order ODE. Surprisingly, we are able to discover such an ODE for the frac
Externí odkaz:
http://arxiv.org/abs/2109.05647
Publikováno v:
Phys. D 388 (2019), 22--32
For a diblock copolymer with total chain length $\gamma>0$ and mass ratio $m\in(-1,1)$, we consider the problem of minimizing the doubly nonlocal free energy $$ \mathcal{E}_{\varepsilon}(u) =\mathcal{H}(u) +\frac{1}{\varepsilon^{2s}} \int_{\Omega}W(u
Externí odkaz:
http://arxiv.org/abs/2011.06907
The standard problem for the classical heat equation posed in a bounded domain $\Omega$ of $\mathbb R^n$ is the initial and boundary value problem. If the Laplace operator is replaced by a version of the fractional Laplacian, the initial and boundary
Externí odkaz:
http://arxiv.org/abs/2007.13391
Publikováno v:
Journal of Functional Analysis, 280 (7), 2021
We develop a linear theory of very weak solutions for nonlocal eigenvalue problems $\mathcal L u = \lambda u + f$ involving integro-differential operators posed in bounded domains with homogeneous Dirichlet exterior condition, with and without singul
Externí odkaz:
http://arxiv.org/abs/2004.04579
We establish uniqueness of vanishing radially decreasing entire solutions, which we call ground states, to some semilinear fractional elliptic equations. In particular, we treat the fractional plasma equation and the supercritical power nonlinearity.
Externí odkaz:
http://arxiv.org/abs/2003.01093
Autor:
Chan, Hardy, DelaTorre, Azahara
We answer affirmatively a question of Aviles posed in 1983, concerning the construction of singular solutions of semilinear equations without using phase-plane analysis. Fully exploiting the semilinearity and the stability of the linearized operator
Externí odkaz:
http://arxiv.org/abs/1912.10352