Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Jeon, Seongmin"'
Autor:
Jeon, Seongmin, Shahgholian, Henrik
In this paper, we study a parabolic free boundary problem in an exterior domain $$\begin{cases} F(D^2u)-\partial_tu=u^a\chi_{\{u>0\}}&\text{in }(\mathbb R^n\setminus K)\times(0,\infty),\\ u=u_0&\text{on }\{t=0\},\\ |\nabla u|=u=0&\text{on }\partial\O
Externí odkaz:
http://arxiv.org/abs/2402.02991
In this paper, we study degenerate or singular elliptic equations in divergence form $$-\text{div}(x_n^\alpha A\nabla u)=\text{div}(x_n^\alpha \mathbf{g})\quad\text{in }B_1\cap\{x_n>0\}.$$ When $\alpha>-1$, we establish boundary Schauder type estimat
Externí odkaz:
http://arxiv.org/abs/2311.06846
Autor:
Jeon, Seongmin, Vita, Stefano
Publikováno v:
J. Differential Equations 412 (2024), 808-856
Aim of this paper is to provide higher order boundary Harnack principles [De Silva-Savin 15] for elliptic equations in divergence form under Dini type regularity assumptions on boundaries, coefficients and forcing terms. As it was proven in [Terracin
Externí odkaz:
http://arxiv.org/abs/2305.05535
Autor:
Jeon, Seongmin, Shahgholian, Henrik
We consider a free boundary problem in an exterior domain \begin{cases}\begin{array}{cc} Lu=g(u) & \text{in }\Omega\setminus K, \\ u=1 & \text{on }\partial K,\\ |\nabla u|=0 &\text{on }\partial \Omega, \end{array}\end{cases} where $K$ is a (given) co
Externí odkaz:
http://arxiv.org/abs/2211.10434
Autor:
Jeon, Seongmin, Petrosyan, Arshak
In this paper, we study almost minimizers for the parabolic thin obstacle (or Signorini) problem with zero obstacle. We establish their $H^{\sigma,\sigma/2}$-regularity for every $0<\sigma<1$, as well as $H^{\beta,\beta/2}$-regularity of their spatia
Externí odkaz:
http://arxiv.org/abs/2209.01565
We study vector-valued almost minimizers of the energy functional $$\int_D\left(|\nabla\mathbf{u}|^2+\frac2{1+q}\left(\lambda_+(x)|\mathbf{u}^+|^{q+1}+\lambda_-(x)|\mathbf{u}^-|^{q+1}\right)\right)dx,\quad0
Externí odkaz:
http://arxiv.org/abs/2207.06217
In this paper we prove radial symmetry for solutions to a free boundary problem with a singular right hand side, in both elliptic and parabolic regime. More exactly, in the unit ball $B_1$ we consider a solution to the fully nonlinear elliptic proble
Externí odkaz:
http://arxiv.org/abs/2207.01157
In this paper we study vector-valued almost minimizers of the energy functional $$ \int_D\left(|\nabla\mathbf{u}|^2+2|\mathbf{u}|\right)\,dx . $$ We establish the regularity for both minimizers and the "regular" part of the free boundary. The analysi
Externí odkaz:
http://arxiv.org/abs/2112.00676
Autor:
Jeon, Seongmin, Vita, Stefano
Publikováno v:
In Journal of Differential Equations 15 December 2024 412:808-856
We study almost minimizers for the thin obstacle problem with variable H\"older continuous coefficients and zero thin obstacle and establish their $C^{1,\beta}$ regularity on the either side of the thin space. Under an additional assumption of quasis
Externí odkaz:
http://arxiv.org/abs/2007.07349