CSpace  > 数学所
projectivedirichletboundaryconditionwithapplicationstoageometricproblem
Ji Min
2016
Source Publicationactamathematicasinicaenglishseries
ISSN1439-8516
Volume32Issue:1Pages:11
AbstractGiven a domain Omega subset of R-n, let lambda > 0 be an eigenvalue of the elliptic operator L := Sigma(n)(i,j=1) partial derivative/partial derivative x(i) (a(ij) partial derivative/partial derivative x(j)) on Omega for Dirichlet condition. For a function f is an element of L-2 (Omega), it is known that the linear resonance equation Lu + lambda u - f in Omega with Dirichlet boundary condition is not always solvable. We give a new boundary condition P-lambda(u vertical bar partial derivative Omega) = g, called to be projective Dirichlet condition, such that the linear resonance equation always admits a unique solution u being orthogonal to all of the eigenfunctions corresponding to lambda which satisfies parallel to u parallel to(2,2) <= C(parallel to f parallel to(2) + parallel to g parallel to(2,2)) under suitable regularity assumptions on partial derivative Omega and L, where C is a constant depends only on n, Omega, and L. More a priori estimates, such as W-2,W-p-estimates and the C-2,C-alpha-estimates etc., are given also. This boundary condition can be viewed as a generalization of the Dirichlet condition to resonance equations and shows its advantage when applying to nonlinear resonance equations. In particular, this enables us to find the new indicatrices with vanishing mean (Cartan) torsion in Minkowski geometry. It is known that the geometry of indicatries is the foundation of Finsler geometry.
Language英语
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/39152
Collection数学所
Affiliation中国科学院数学与系统科学研究院
Recommended Citation
GB/T 7714
Ji Min. projectivedirichletboundaryconditionwithapplicationstoageometricproblem[J]. actamathematicasinicaenglishseries,2016,32(1):11.
APA Ji Min.(2016).projectivedirichletboundaryconditionwithapplicationstoageometricproblem.actamathematicasinicaenglishseries,32(1),11.
MLA Ji Min."projectivedirichletboundaryconditionwithapplicationstoageometricproblem".actamathematicasinicaenglishseries 32.1(2016):11.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Ji Min]'s Articles
Baidu academic
Similar articles in Baidu academic
[Ji Min]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Ji Min]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.