Sobolev space theory of parabolic equations degenerating on the boundary of C1 domains

被引：14

作者：

Kim, Kyeong-Hun ^{[1
]}

机构：

[1] Korea Univ, Dept Math, Seoul 136701, South Korea

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2007年 / 32卷 / 7-9期

关键词：

C-1; domains; degenerate parabolic equations; Sobolev spaces with weights;

D O I：

10.1080/03605300600910449

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Second-order parabolic equations degenerating on the boundary of C-1 domains are considered. Existence and uniqueness results are given in weighted Sobolev spaces, and Holder estimates of the solutions are presented.

引用

页码：1261 / 1280

页数：20

共 50 条

[31] Boundary Value Problems for Parabolic Equations in Noncylindrical Domains
E. M. Kartashov
High Temperature, 2022, 60 : 662 - 676
[32] A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients
Skrypnik I.I.
Ukrainian Mathematical Journal, 2004, 56 (6) : 973 - 995
[33] A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients
I. I. Skrypnik
Ukrainian Mathematical Journal, 2004, 56 (6) : 973 - 995
[34] On the First Mixed Problem in Lp, p > 1, for the Degenerating on the Boundary Parabolic Equations of Second Order
Petrushko, Igor M.
Petrushko, Maxim I.
PROCEEDINGS OF THE 44TH INTERNATIONAL CONFERENCE "APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS", 2018, 2048
[35] Sobolev space theory and Holder estimates for the stochastic partial differential equations on conic and polygonal domains
Kim, Kyeong-Hun
Lee, Kijung
Seo, Jinsol
JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 340 : 463 - 520
[36] Regularity for Robin boundary problems of Laplace equations and Hardy spaces on C1 and (semi-)convex domains
Yang, Sibei
Sickel, Winfried
Yang, Dachun
Yuan, Wen
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 279 : 198 - 244
[37] On stochastic partial differential equations with variable coefficients in C1 domains
Kim, KH
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2004, 112 (02) : 261 - 283
[38] Volume of C1,α-boundary domain in extended hyperbolic space
Cho, Yunhi
Kim, Hyuk
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2006, 43 (06) : 1143 - 1158
[39] Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant
Tolsa, Xavier
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2023, 76 (02) : 305 - 336
[40] C1,α-regularity for solutions of degenerate/singular fully nonlinear parabolic equations
Lee, Ki-Ahm
Lee, Se-Chan
Yun, Hyungsung
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2024, 181 : 152 - 189

← 1 2 3 4 5 →