Zobrazeno 1 - 10
of 144
pro vyhledávání: '"KIM, SEICK"'
Autor:
Gyöngy, Istvan, Kim, Seick
This paper investigates the Harnack inequality for nonnegative solutions to second-order parabolic equations in double divergence form. We impose conditions where the principal coefficients satisfy the Dini mean oscillation condition in $x$, while th
Externí odkaz:
http://arxiv.org/abs/2405.04482
This paper investigates the Dirichlet problem for a non-divergence form elliptic operator $L$ in a bounded domain of $\mathbb{R}^d$. Under certain conditions on the coefficients of $L$, we first establish the existence of a unique Green's function in
Externí odkaz:
http://arxiv.org/abs/2402.17948
We investigate the regularity of elliptic equations in double divergence form, with leading coefficients satisfying the Dini mean oscillation condition. We prove that the solutions are differentiable on the zero level set and derive a pointwise bound
Externí odkaz:
http://arxiv.org/abs/2401.06621
Autor:
Kim, Seick, Sakellaris, Georgios
Publikováno v:
Calculus of Variations and Partial Differential Equations 63 (2024), no. 8, Paper No. 219, 45 pp
We construct the Neumann Green function and establish scale invariant regularity estimates for solutions to the Neumann problem for the elliptic operator $Lu=-{\rm div}({\bf A} \nabla u+ \boldsymbol{b}u)+ \boldsymbol{c} \cdot \nabla u+du$ in a Lipsch
Externí odkaz:
http://arxiv.org/abs/2302.00132
Publikováno v:
Journal of Machine Learning Research 23 (2022) 1-34
Neural operators are a popular technique in scientific machine learning to learn a mathematical model of the behavior of unknown physical systems from data. Neural operators are especially useful to learn solution operators associated with partial di
Externí odkaz:
http://arxiv.org/abs/2204.12789
Publikováno v:
Journal of Differential Equations 340 (2022), no. 1, 557-591
We construct the fundamental solution of second order parabolic equations in non-divergence form under the assumption that the coefficients are of Dini mean oscillation in the spatial variables. We also prove that the fundamental solution satisfies a
Externí odkaz:
http://arxiv.org/abs/2201.03811
Publikováno v:
Proceedings of the American Mathematical Society 151 (2023), no.5, 2045-2055
We improve a result in Kim and Lee (Ann. Appl. Math. 37(2):111--130, 2021): showing that if the coefficients of an elliptic operator in non-divergence form are of Dini mean oscillation, then its Green's function has the same asymptotic behavior near
Externí odkaz:
http://arxiv.org/abs/2201.03764
Autor:
Kim, Seick, Lee, Sungjin
Publikováno v:
Annals of Applied Mathematics 37 (2021), no. 2, 111-130
We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients. We also present a sharp comparison with the corresponding Green's function for c
Externí odkaz:
http://arxiv.org/abs/2103.04071
Autor:
Kim, Seick, Xu, Longjuan
Publikováno v:
Communications on Pure and Applied Analysis, Vol. 21 (2022), no. 1, pp. 1-21
We construct Green's functions for second order parabolic operators of the form $Pu=\partial_t u-{\rm div}({\bf A} \nabla u+ \boldsymbol{b}u)+ \boldsymbol{c} \cdot \nabla u+du$ in $(-\infty, \infty) \times \Omega$, where $\Omega$ is an open connected
Externí odkaz:
http://arxiv.org/abs/2009.04133
Autor:
Dong, Hongjie, Kim, Seick
Publikováno v:
SIAM Journal on Mathematical Analysis, 53 (2021), no.4, pp. 4637-4656
We construct the Green function for second-order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that the Green's function is BMO in the domain and establish logarithmic poi
Externí odkaz:
http://arxiv.org/abs/2003.11185