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REMARKS ON SINGULAR TRUDINGER-MOSER TYPE INEQUALITIES
文献类型：期刊
通讯作者：Zhu, XB (reprint author), Renmin Univ China, Sch Math, Beijing 100872, Peoples R China.
期刊名称：COMMUNICATIONS ON PURE AND APPLIED ANALYSIS影响因子和分区
年：2020
卷：19
期：1
页码：103-112
ISSN：1534-0392
关键词：Singular Trudinger-Moser type inequality; extremal function; convex symmetrization
摘要：Let Omega subset of R-n be a bounded domain. Let F : R-n -> [0, +infinity) be a convex function of class C-2(R-n\{0}), which is even and positively homogeneous of degree 1. For such a function F, there exist two positive constants a(1) <= a(2) such that a(1) vertical bar xi vertical bar <= F(xi) <= a(2)vertical bar xi vertical bar (for all xi is an element of R-n). Therefore, (integral(Omega) F(del u)(n)dx)(1/n) and (integral(n)(R)(F del u)(n)dx)(1/n)(tau > 0) are equivalent with the standard no ...More
Let Omega subset of R-n be a bounded domain. Let F : R-n -> [0, +infinity) be a convex function of class C-2(R-n\{0}), which is even and positively homogeneous of degree 1. For such a function F, there exist two positive constants a(1) <= a(2) such that a(1) vertical bar xi vertical bar <= F(xi) <= a(2)vertical bar xi vertical bar (for all xi is an element of R-n). Therefore, (integral(Omega) F(del u)(n)dx)(1/n) and (integral(n)(R)(F del u)(n)dx)(1/n)(tau > 0) are equivalent with the standard norms on W-0(1,n)(Omega) and W-1,W-n(R-n) respectively. In this paper, we prove that sup (u is an element of W01,n(Omega),integral Omega F(del u)ndx <= 1)integral(Omega) e(lambda vertical bar u vertical bar n/n-1)/F-0(x)(beta)dx < +infinity double left right arrow lambda/lambda(n )+ beta/n <= 1( ) and sup (u is an element of W1, n (Rn),integral Rn (F(del u)n+tau vertical bar u vertical bar n)dx <= 1)integral(Rn) e(lambda vertical bar u vertical bar n/n-1) - Sigma(n-2)(k=0)lambda(k)vertical bar u vertical bar(nk/n-1)/k!/F-0(x)(beta)dx < infinity double left right arrow lambda/lambda(n) + beta/n <= 1, where F-0 is the polar function of F, lambda > 0, beta is an element of [0,n), tau > 0, lambda(n) = n(n/n-1)K(n)(1/n-1) and K-n is the volume of the unit Wulff ball. Extremal functions for above two supremums are also considered. ...Hide

DOI：10.3934/cpaa.2020006
百度学术：REMARKS ON SINGULAR TRUDINGER-MOSER TYPE INEQUALITIES
语言：外文
基金：National Science Foundation of ChinaNational Natural Science Foundation of China [11401575]
作者其他论文



A Trudinger-Moser inequality for a conical metric in the unit ball.Yang, Yunyan, Zhu, Xiaobao,.ARCHIV DER MATHEMATIK. 2019, 112(5), 531-545.
A generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularities.Zhu, Xiaobao,.SCIENCE CHINA-MATHEMATICS. 2019, 62(4), 699-718.
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.
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.