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A generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularities
文献类型：期刊
通讯作者：Zhu, XB (reprint author), Renmin Univ China, Dept Math, Beijing 100872, Peoples R China.
期刊名称：SCIENCE CHINA-MATHEMATICS影响因子和分区
年：2019
卷：62
期：4
页码：699-718
ISSN：1674-7283
关键词：Trudinger-Moser inequality; the extremal function; blow-up analysis; conical singularity
所属部门：信息学院
摘要：In this paper, using the method of blow-up analysis, we establish a generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularity. Precisely, let (Sigma,D) be such a surface with divisor D = Sigma(m)(i=1) beta(i)p(i), where beta(i) > -1 and p(i) is an element of Sigma for i = 1, ... , m, and g be a metric representing D. Denote b(0) = 4 pi(1 + min(1 <= i <= m beta i)). Suppose psi : Sigma -> R is a continuous function with integral(Sigma)psi dv(g) not equal 0 an ...More
In this paper, using the method of blow-up analysis, we establish a generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularity. Precisely, let (Sigma,D) be such a surface with divisor D = Sigma(m)(i=1) beta(i)p(i), where beta(i) > -1 and p(i) is an element of Sigma for i = 1, ... , m, and g be a metric representing D. Denote b(0) = 4 pi(1 + min(1 <= i <= m beta i)). Suppose psi : Sigma -> R is a continuous function with integral(Sigma)psi dv(g) not equal 0 and define lambda(1)**(Sigma, g) = inf(u is an element of H1(Sigma, g), integral Sigma psi udvg = 0, integral Sigma u2dvg = 1) integral(Sigma)vertical bar del(g)u vertical bar(2)dv(g). Then for any alpha is an element of[0,lambda(1)** (Sigma,g)), we have sup(u is an element of H1(Sigma, g), integral Sigma psi u=0, integral Sigma vertical bar del gu vertical bar 2dvg) (- alpha integral Sigma u2dvg <= 1) integral(Sigma) e(b0u2)dv(g) < + infinity. When b > b(0), the integrals integral(Sigma)c(bu2)dv(g) are still finite, but the supremum is infinity. Moreover, we prove that the extremal function for the above inequality exists. ...Hide

DOI：10.1007/s11425-017-9174-2
百度学术：A generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularities
语言：外文
被引频次：1
基金：National Natural Science Foundation of ChinaNational Natural Science Foundation of China [11401575]
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A Trudinger-Moser inequality for a conical metric in the unit ball.Yang, Yunyan, Zhu, Xiaobao,.ARCHIV DER MATHEMATIK. 2019, 112(5), 531-545.
PRESCRIBING GAUSSIAN CURVATURE ON CLOSED RIEMANN SURFACE WITH CONICAL SINGULARITY IN THE NEGATIVE CASE.Yang, Yunyan, Zhu, Xiaobao,.ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA. 2019, 44, 167-181.
REMARKS ON SINGULAR TRUDINGER-MOSER TYPE INEQUALITIES.Zhu, Xiaobao,.COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. 2020, 19(1), 103-112.
Trudinger-Moser Embedding on the Hyperbolic Space.Yang, Yunyan;Zhu, Xiaobao.ABSTRACT AND APPLIED ANALYSIS.2014.
Hamilton's gradient estimates and Liouville theorems for porous medium equations on noncompact Riemannian manifolds.Zhu, Xiaobao.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS.2013,402(1),201-206.