On a class of evolution equations in Lipschitz subdomains of Riemannian manifolds

被引：0

作者：

de Andrade, Bruno ^{[1
]}

机构：

[1] Univ Fed Sergipe, Dept Matemat, Sao Cristovao, SE, Brazil

来源：

APPLICABLE ANALYSIS | 2024年

关键词：

Evolutionary integrodifferential equations; fractional kernels; Hodge-Laplacian; Lipschitz domains; FRACTIONAL DIFFERENTIAL-EQUATIONS; NAVIER-STOKES EQUATIONS; BOUNDARY-CONDITIONS; HODGE LAPLACIAN; CAUCHY-PROBLEMS;

D O I：

10.1080/00036811.2024.2426086

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence, uniqueness, analyticity, and continuous dependence of mild solutions for a class of evolutionary integrodifferential equations with free boundary conditions on $ L<^>p $ Lp-spaces in Lipschitz subdomains of Riemannian manifolds. Our strategy is to use the Laplace transform theory to ensure the existence of an analytic resolvent to the Hodge-Laplacian in the space of all & ell;-differential forms with p-th power integrable coefficients.

引用

页数：13

共 50 条

[1] RIESZ TRANSFORMS ASSOCIATED WITH THE HODGE LAPLACIAN IN LIPSCHITZ SUBDOMAINS OF RIEMANNIAN MANIFOLDS
Hofmann, Steve
Mitrea, Marius
Monniaux, Sylvie
ANNALES DE L INSTITUT FOURIER, 2011, 61 (04) : 1323 - 1349
[2] Navier-Stokes equations on Lipschitz domains in Riemannian manifolds
Marius, M
Taylor, M
MATHEMATISCHE ANNALEN, 2001, 321 (04) : 955 - 987
[3] Navier-Stokes equations on Lipschitz domains in Riemannian manifolds
Marius Mitrea
Michael Taylor
Mathematische Annalen, 2001, 321 : 955 - 987
[4] ON A CLASS OF HESSIAN TYPE EQUATIONS ON RIEMANNIAN MANIFOLDS
Jiao, Heming
Liu, Jinxuan
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 151 (02) : 569 - 581
[5] On a class of obstacle problem for Hessian equations on Riemannian manifolds
Liu, Jinxuan
Wang, Yong
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2023, 2023 (01)
[6] On a class of nonhomogeneous elliptic equations on noncompact Riemannian manifolds
de Souza, Manasses
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2019, 64 (03) : 386 - 397
[7] ON A CLASS OF HESSIAN QUOTIENT TYPE EQUATIONS ON RIEMANNIAN MANIFOLDS
Liang, Weizhao
Zhu, Hua
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (01) : 307 - 318
[8] On a class of obstacle problem for Hessian equations on Riemannian manifolds
Jinxuan Liu
Yong Wang
Journal of Inequalities and Applications, 2023
[9] ON THE ANALYTICITY OF THE SEMIGROUP GENERATED BY THE STOKES OPERATOR WITH NEUMANN-TYPE BOUNDARY CONDITIONS ON LIPSCHITZ SUBDOMAINS OF RIEMANNIAN MANIFOLDS
Mitrea, Marius
Monniaux, Sylvie
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (06) : 3125 - 3157
[10] LIPSCHITZ CONVERGENCE OF RIEMANNIAN-MANIFOLDS
GREENE, RE
WU, H
PACIFIC JOURNAL OF MATHEMATICS, 1988, 131 (01) : 119 - 141

← 1 2 3 4 5 →