2024 Kazdan-warner type equation

Kazdan-warner type equation

Author: xmwu

August undefined, 2024

WebbThe Kazdan-Warner type identity is derived from the divergence structure as below n−k n < X,∇σk(g−1A) >= ∇b(XaH˚b a). For k = 1, it has been proved by Schoen [Sc2] and applied to prove the existence of the singular Yamabe problem. The Kazdan-Warner identity was also used to the Yamabe problem on star-shaped domain by Webb19 juni 2024 · We finally provide some applications of our main results by dealing with some Yamabe-type and Kazdan-Warner-type equations on locally finite weighted graphs. Submission history From: Giorgio Stefani [ view email ] [v1] Sat, 19 Jun 2024 07:57:08 UTC (14 KB) Download: PDF PostScript Other formats ( license) Current …

EXISTENCE AND UNIQUENESS THEOREMS FOR SOME SEMI-LINEAR EQUATIONS …

Webb18 juli 2016 · The Kazdan–Warner equation on graph reads \begin {aligned} \Delta u=c-he^u\quad \mathrm {in}\quad V, \end {aligned} (7) where \Delta is defined as in ( 3 ), c\in \mathbb {R}, and h:V\rightarrow \mathbb {R} is a function. If c=0, then ( 7) is reduced to \begin {aligned} \Delta u=-he^u\quad \mathrm {in}\quad V. \end {aligned} (8) Webb19 juni 2024 · When $m=1$, we also establish a uniqueness result in the spirit of the Brezis-Strauss Theorem. We finally provide some applications of our main results by dealing with some Yamabe-type and... ridgeview global studies academy soccer

A NOTE ON THE KAZDAN-WARNER TYPE CONDITIONS

Webb20 feb. 2024 · The Kazdan–Warner equation was generalized by Ge and Jiang to certain infinite graphs. Recently, many results also have been obtained for parabolic equations on graphs. The blow-up phenomenon of the semilinear heat equation was studied by Lin and Wu [13, 21] on locally finite graphs. Lin and Yang proposed a heat flow for the mean … Webb16 juli 2024 · A class of semilinear equations with the exponential nonlinearity, so-called Kazdan-Warner equations and the Liouville equations, also have been studied in these papers [15,18,19,23,32,44] on ... Webb1 okt. 2024 · Consider the p-th Kazdan–Warner equation on G Δ p u = c − h e u, where Δ p is the discrete p-Laplacian on G with p > 1, h is a known function defined on V. When c < 0 and h ‾ < 0, Ge [8] showed that there exists a negative number c − (h) such that the p-th Kazdan–Warner equation on G is solvable for every 0 > c > c − (h ... ridgeview gaylord clinic

Another remark on a result of Ding-Jost-Li-Wang

The pth Kazdan–Warner equation on graphs Communications in ...

http://math.tju.edu.cn/info/1622/7331.htm Webb24 jan. 2024 · We consider the following Kazdan–Warner equation \begin {aligned} -\Delta _ {g}u=8\pi \left ( \dfrac {he^ {u}} {\int _ {\Sigma }he^ {u}\mathop {}\mathrm {d}\mu _ {g}}-1\right) . \end {aligned} (1.1) Here \Delta _ {g} is the Laplace–Beltrami operator. The solutions to ( 1.1) are the critical points of the following functional: ridgeview golf course grouponWebb3 juni 2008 · In this paper, we discuss a Kazdan-Warner typed equation on certain non-compact Riemannian manifolds. As an application, we prove an existence theorem of Hermitian-Yang-Mills-Higgs metrics on holomorphic line bundles over certain non-compact Kähler manifolds. Download to read the full article text. ridgeview gibsonia

"WebbKAZDAN-WARNER PROBLEM ON COMPACT RIEMANN SURFACES WITH SMOOTH BOUNDARY JIE XU ... and M. Rigoli. Yamabe type equations with a sign-changing nonlinearity, and the pre-scribed curvature problem. Journal of Diﬀerential Equations, 260(10):7416–7497, 2016. [4] J. Bourguignon and J. Ezin. Scalar curvature functions in … " - Kazdan-warner type equation

Kazdan-warner type equation

(Open Access) A complete conformal metric of preassigned …

Webb1 juni 2024 · In seventies of the last century, by releasing the geometric restriction, Kazdan and Warner [ 20] initiated the study of the semi-linear equation \begin {aligned} -\Delta _gu=he^u-\rho \end {aligned} (1.2) where \rho is a constant and h … Webb28 nov. 2016 · the Kazdan-Warner equation solvable for $c=c_- (h)$? \end {center} In this paper, we answer the question affirmatively. We show that if , then and . Moreover, if , then there exists at least one solution to the Kazdan-Warner equation with . Submission history From: Ge Huabin [ view email ] [v1] Mon, 28 Nov 2016 15:28:05 UTC (5 KB)

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Webb1 apr. 2006 · Une identité de type Kazdan–Warner pour la. σ. k. -courbure. We prove a Kazdan–Warner type identity involving the σ k curvature and a conformal Killing vector field on a compact manifold. Our method also works to provide a unified proof for the necessary conditions in the Christoffel–Minkowski problem. Webb10 apr. 2024 · This leads us to a Liouville-type equation with a non-linear Neumann boundary condition. We address the question of existence by setting the problem in a variational framework which seems to be ...

Webb31 jan. 2024 · Remark 4.1 Using the reduced, static Keller–Segel equation also, equations similar to the Kazdan–Warner equation were studied in [Reference Bonheure, Casteras and Noris 3, Reference Wang, Wang and Yang 9]. These equations however are still on the plane so the geometric interpretation above is lost. Webb1 sep. 2024 · Kazdan–Warner equation on graph A. Grigor’yan, Yong Lin, Y. Yang Mathematics 2016 Let $$G= (V,E)$$G= (V,E) be a connected finite graph and $$\Delta $$Δ be the usual graph Laplacian. Using the calculus of variations and a method of upper and lower solutions, we give various… Expand 76 PDF

Webb23 dec. 2024 · In this paper, we study the following Kazdan-Warner equation with sign-changing prescribed function h −∆u = 8π View PDF on arXiv Save to Library Create Alert Cite 4 Citations Citation Type More Filters Another remark on a result of Ding-Jost-Li …

Webb12 mars 2024 · A class of semilinear equations with the exponential nonlinearity, so-called Kazdan-Warner equations and the Liouville equations, also have been studied in these papers [15,18, 19,...

Webb10 apr. 2024 · Jie Xu. In this article, we show that (i) any smooth function on compact Riemann surface with non-empty smooth boundary can be realized as a Gaussian curvature function; (ii) any smooth function on can be realized as a geodesic curvature function for some metric . The essential steps are the existence results of Brezis-Merle … ridgeview gastroenterology waconiaWebbOn a Paneitz Type Equation in Six Dimensional Domains Sur une ´equation de type Paneitz dans les domaines de dimension six Hichem CHTIOUIa & Khalil EL MEHDIb,c ∗ a : D´epartement de Math´ematiques, Facult´e des Sciences de Sfax, Route Soukra, Sfax, Tunisia. E-mail : [email protected] ridgeview global academyWebb13 apr. 2024 · Abstract: In this talk, we shall review firstly the study history of Kazdan-Warner equations on compact Riemann surfaces, which was proposed by Kazdan and Warner on Annals of Math on 1974. Then we shall show the sufficient condition which was derived by Ding-Jost-Li-Wang (Asian J. Math.,1997). Finally, we shall present our new … ridgeview florist allenWebb1 juni 2008 · In the beginning, the Kazdan-Warner equation, Δ g u = c − he u (refer to [2,3, [13] [14] [15] [16] ), describes a conformal deformation on the smooth metric g on a 2-dimensional closed... ridgeview golf courseWebb16 mars 2024 · The Kazdan–Warner equation arises from the basic geometric question which functions are potential Gaussian curvatures of 2-dimensional manifolds. Kazdan and Warner studied this question on compact manifolds [ 29] and on open manifolds that are diffeomorphic to an open set in a compact manifold [ 30 ]. ridgeview gastroenterology chaskaWebb1 juni 2024 · Let G=(V,E) be a connected finite graph. Consider the p-th Kazdan–Warner equation on G Δpu=c−heu, where Δp is the discrete p-Laplacian on G with p>1, h is a known function defined on V. ridgeview golf course ligonier paWebbDifferent from the variational methods often used in the finite graph case, we use a heat flow method to study the graph Kazdan-Warner equation. We prove the existence of a solution to the graph Kazdan-Warner equation under the assumption that $h\leq0$ and some other integrability conditions or constrictions about the underlying infinite graphs. ridgeview golf course plano