GLOBAL WELL-POSEDNESS OF STRONG SOLUTIONS TO A TROPICAL CLIMATE

doi:10.3934/dcds.2016.36.4517

CORC > 上海财经大学 > 上海财经大学

	GLOBAL WELL-POSEDNESS OF STRONG SOLUTIONS TO A TROPICAL CLIMATE
	Lin, Fanghua 1; Liu, Dan 2,3
刊名	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
	2016-08
卷号	36 期号:8 页码:4517-4529
关键词	Betti number level set nodal set elliptic PDEs
ISSN号	1078-0947
DOI	10.3934/dcds.2016.36.4517
英文摘要	In this paper we study the topological properties of the level sets, (t)(u) = {x : u(x) = t}, of solutions u of second order elliptic equations with vanishing zeroth order terms. We show that the total Betti number of level sets x t is a uniformly bounded function of the parameter t. The uniform bound can be estimated in terms of the analytic coe ffi cients as well as the generalized degrees of the corresponding solutions. Such an estimate is also valid for the nodal sets of solutions of the same type equations with zeroth order terms. In general, it is possible to derive from our analysis an estimate for the total Betti numbers of level sets, for large measure set of t's, when coe ffi cients are su ffi ciently smooth, and therefore a L p bound on Betti numbers as a function of t. These estimates are obtained by a quantitative Stability Lemma and a quantitative Morse Lemma.
WOS研究方向	Mathematics
语种	英语
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
WOS记录号	WOS:000372000300018
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/1248]
专题	上海财经大学
作者单位	1.NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA; 2.E China Normal Univ, Ctr Partial Differential Equat, Shanghai 200062, Peoples R China; 3.Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Lin, Fanghua,Liu, Dan. GLOBAL WELL-POSEDNESS OF STRONG SOLUTIONS TO A TROPICAL CLIMATE[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2016,36(8):4517-4529.
APA	Lin, Fanghua,&Liu, Dan.(2016).GLOBAL WELL-POSEDNESS OF STRONG SOLUTIONS TO A TROPICAL CLIMATE.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,36(8),4517-4529.
MLA	Lin, Fanghua,et al."GLOBAL WELL-POSEDNESS OF STRONG SOLUTIONS TO A TROPICAL CLIMATE".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 36.8(2016):4517-4529.