Kazdan-warner type equation

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August undefined, 2024

WebbWith the help of these results, we finally give various conditions such that the p th Kazdan–Warner equation Δ p u = c − h e u has a solution on V for given h ∈ C (V) and c ∈ ℝ. Thus we generalize Grigor’yan, Lin and Yang’s work Kazdan–Warner equation on graph, Calc. Var. Partial Differential Equations 55 (4) (2016) Paper No ... Webb13 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 …

p-th Kazdan–Warner equation on graph in the negative …

WebbSearch 211,578,062 papers from all fields of science. Search. Sign In Create Free Account Create Free Account 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 … cert 2 in rail infrastructure

Stationary solutions to the Keller–Segel equation on curved …

WebbOn 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] Webb1 okt. 2024 · In the beginning, the Kazdan–Warner equation, Δ g u = c − h e u (refer to [2], [3], [13], [14], [15], [16] ), describes a conformal deformation on the smooth metric g on a 2-dimensional closed Riemannian manifold ( M, g), with both c and h are independent of the geometry of ( M, g), where c is a constant and h is some stipulated function. 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 ... cert 2 in creative industries

Kazdan–Warner equation on graph SpringerLink

On Maxwell’s Equations with a Magnetic Monopole on Manifolds

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. 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... cert 2 in civil constructionWebb15 juli 2016 · p-th Kazdan-Warner equation on graph Huabin Ge Mathematics 2016 Let $G= (V,E)$ be a connected finite graph and $C (V)$ be the set of functions defined on $V$. Let $\Delta_p$ be the discrete $p$-Laplacian on $G$ with $p>1$ and $L=\Delta_p-k$, where $k\in C (V)$ is… Expand 7 PDF Positive Solutions of p-th Yamabe Type … cert 2 in hairdressing

"Webb28 dec. 2024 · We consider a generalization of Maxwell’s equations on a pseudo-Riemannian manifold M of arbitrary dimension in the presence of electric and magnetic charges and prove that if the cohomology groups H2 ( M) and H3 ( M) are trivial, then solving these equations reduces to solving the d’Alembert—Hodge equation. … " - Kazdan-warner type equation

Kazdan-warner type equation

The Kazdan–Warner equation on canonically compactifiable graphs

http://math.tju.edu.cn/info/1622/7331.htm 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.

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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: WebbIn order to apply the method of moving planes to equation (*), it requires the function R be monotone decreasing. However, we want our R to satisfy conditions of Kazdan-Warner type; hence it must not be monotone in the whole domain. To circumvent this difficulty, we introduce a new unknown function v(x) = u(x) - \x\2.

Webb18 sep. 2024 · Abstract: We investigate the Kazdan-Warner equation on a network. In this case, the differential equation is defined on each edge, while appropriate transition conditions of Kirchhoff type are prescribed at the vertices. We show that the Kazdan-Warner theory extends to the present setting and we study also the critical case. 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 ...

WebbLeth be a complete metric of Gaussian curvature K0 on a punctured Riemann surface of genusg ≥ 1 (or the sphere with at least three punctures). Given a smooth negative functionK withK =K 0 in neighbourhoods of the punctures we prove that there exists a metric conformal toh which attains this function as its Gaussian curvature for the … 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 …

Webb1 okt. 2024 · p-th Kazdan–Warner equation on graph in the negative case @article{Zhang2024pthKE, title={p-th Kazdan–Warner equation on graph in the negative case}, author={Xiaoxiao Zhang and Yanxun Chang}, journal={Journal of Mathematical Analysis and Applications}, year={2024} } Xiaoxiao Zhang, Yanxun Chang; Published 1 … buy small shed ukWebb10 jan. 2024 · M. Keller and M. Schwarz, “The Kazdan-Warner equation on canonically compactifiable graphs,” Calculus of Variations and Partial Differential Equations, vol. 57, no. 2, p. 70, 2024. View at:Publisher Site Google Scholar N. Zhang and L. Zhao, “Convergence of ground state solutions for nonlinear Schrödinger equations on … cert 2 in salon assistantWebb10 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 … cert 2 in resources and infrastructureWebb28 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) cert 2 resource processingWebbThe 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 buy small septic tankWebb30 sep. 2011 · In this paper, we establish existence results for positive solutions to the Lichnerowicz equations of the following type in closed manifolds -\Delta u = A (x)u^ {-p} - B (x)u^ {q},\quad { {\rm in}}\, M, where p > 1, q > 0, and A ( x ) > 0, B ( x ) ≥ 0 are given smooth functions. buy small sewing machineWebbThe Kazdan-Warner Type equations I am talking about is the following: Suppose X be a compact Riemannian manifold (of any dimension) and A, B, and w to be smooth function, I hope to know more about the known result to the following equation: Δ u + A e u − B e − u − w = 0 Here is my questions: cert 2 in visual arts