Zobrazeno 1 - 10
of 8 127
pro vyhledávání: '"A Ahm"'
We develop the viscosity method for the homogenization of an obstacle problem with highly oscillating obstacles. The associated operator, in non-divergence form, is linear and elliptic with variable coefficients. We first construct a highly oscillati
Externí odkaz:
http://arxiv.org/abs/2410.09378
We prove the Wolff potential estimates for nonlocal equations with Orlicz growth. As an application, we obtain the Wiener criterion in this framework, which provides a necessary and sufficient condition for boundary points to be regular. Our approach
Externí odkaz:
http://arxiv.org/abs/2312.16411
Autor:
Lee, Ki-Ahm, Lee, Taehun
We consider a flow by powers of Gauss curvature under the obstruction that the flow cannot penetrate a prescribed region, so called an obstacle. For all dimensions and positive powers, we prove the optimal curvature bounds of solutions and all time e
Externí odkaz:
http://arxiv.org/abs/2310.02668
Autor:
Lee, Ki-Ahm, Lee, Taehun
In this paper, we investigate energy-minimizing curves with fixed endpoints $p$ and $q$ in a constrained space. We prove that when one of the endpoints, say $p$, is fixed, the set of points $q$ for which the energy-minimizing curve is not unique has
Externí odkaz:
http://arxiv.org/abs/2306.07511
Autor:
Lee, Ki-Ahm, Yun, Hyungsung
In this paper, we establish the boundary regularity results for viscosity solutions of fully nonlinear degenerate/singular parabolic equations of the form $$u_t - x_n^{\gamma} F(D^2 u,x,t) = f,$$ where $\gamma<1$. These equations are motivated by the
Externí odkaz:
http://arxiv.org/abs/2305.14615
In this paper, we study generalized Schauder theory for the degenerate/singular parabolic equations of the form $$u_t = a^{i'j'}u_{i'j'} + 2 x_n^{\gamma/2} a^{i'n} u_{i'n} + x_n^{\gamma} a^{nn} u_{nn} + b^{i'} u_{i'} + x_n^{\gamma/2} b^n u_{n} + c u
Externí odkaz:
http://arxiv.org/abs/2304.08734
We establish the interior $C^{1,\alpha}$-estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations $$u_t = |Du|^{\gamma}F(D^2u) + f.$$ For this purpose, we prove the well-posedness of the regularized Dirichlet proble
Externí odkaz:
http://arxiv.org/abs/2303.09059
Autor:
Hooshyar, Hossein, Kadavil, Rahul, Paduani, Victor, Haddadi, Aboutaleb, Jakaria, AHM, Huque, Aminul
This paper presents a case study for utilizing behind-the-meter (BTM) distributed energy resources (DERs) to provide grid services when controlled by a DER Management System (DERMS). The testbed consists of a 5,000 buses transient-stability (TS) real
Externí odkaz:
http://arxiv.org/abs/2302.01123
Autor:
Paduani, Victor, Kadavil, Rahul, Hooshyar, Hossein, Haddadi, Aboutaleb, Jakaria, AHM, Huque, Aminul
This paper presents the development of a real-time T&D co-simulation testbed for simulating large grids under high DER penetration. By integrating bulk power system, distribution feeders, and distributed energy resources (DER) models into one simulat
Externí odkaz:
http://arxiv.org/abs/2302.01120
Autor:
Lee, Ki-Ahm, Lee, Se-Chan
We study the boundary continuity of solutions to fully nonlinear elliptic equations. We first define a capacity for operators in non-divergence form and derive several capacitary estimates. Secondly, we formulate the Wiener criterion, which character
Externí odkaz:
http://arxiv.org/abs/2301.00960