Existence of the heat flow with sign-changing prescribed function

DOI10.1016/j.jmaa.2024.128118OpenAlexW4390753535MaRDI QIDQ6191119

Pengxiu Yu, Yun Yan Yang

Publication date: 6 March 2024

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2024.128118

zbMATH Keywords

heat flowTrudinger-Moser inequalitysign-changing prescribed function

Mathematics Subject Classification ID

Heat and other parabolic equation methods for PDEs on manifolds (58J35) Riemann surfaces (30F99) Elliptic equations and elliptic systems (35Jxx) Global differential geometry (53Cxx)

Cites Work

• A generalized Trudinger-Moser inequality on a compact Riemannian surface
• The heat flow with a critical exponential nonlinearity
• Topological methods for an elliptic equation with exponential nonlinearities
• Prescribing Gaussian curvature on S 2
• Conformal deformations of metric on \({\mathcal S}\) 2
• Classification of solutions of some nonlinear elliptic equations
• Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere
• On a sharp Sobolev-type inequality on two-dimensional compact manifolds
• Existence results for mean field equations
• Double vortex condensates in the Chern-Simons-Higgs theory
• The differential equation \(\Delta u=8\pi-8\pi he^u\) on a compact Riemann surface
• An analysis of the two-vortex case in the Chern-Simons Higgs model
• Topological degree for mean field equations on \(S^2\)
• Existence of solutions to a class of Kazdan-Warner equations on compact Riemannian surface
• The convergence of the mean field type flow at a critical case
• Vortex condensation in the Chern-Simons Higgs model: An existence theorem
• On Gaussian curvature flow
• A mean field type flow with sign-changing prescribed function on a symmetric Riemann surface
• A heat flow for the critical Trudinger-Moser functional on a closed Riemann surface
• A flow approach to mean field equation
• Global existence and convergence of a flow to Kazdan-Warner equation with non-negative prescribed function
• Curvature functions for compact 2-manifolds
• Singularity formation for the two-dimensional harmonic map flow into \(S^2\)
• A mean field type flow. I: compactness of solutions to a perturbed mean field type equation
• Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two
• Ricci flow on surfaces with conic singularities
• A mean field type flow. II: Existence and convergence
• Blow-up of the mean curvature at the first singular time of the mean curvature flow
• The Equation Δ<em>u</em>+∇φ•∇<em>u</em>=8<em>πc</em>(1-<em>he</em>^<em>u</em>) on a Riemann Surface
• Finding critical points of the Trudinger-Moser functional through the heat flow
• EXISTENCE RESULT FOR THE MEAN FIELD PROBLEM ON RIEMANN SURFACES OF ALL GENUSES
• A Best Constant and the Gaussian Curvature
• Scalar Curvatures on S 2
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• Topological degree for a mean field equation on Riemann surfaces
• Sharp estimates for solutions of multi‐bubbles in compact Riemann surfaces
• Mean field equations on a closed Riemannian surface with the action of an isometric group
• A remark on a result of Ding-Jost-Li-Wang
• Multiple condensate solutions for the Chern–Simons–Higgs theory
• ON NIRENBERG'S PROBLEM
• An existence result for the Kazdan-Warner equation with a sign-changing prescribed function
• A singular Kazdan-Warner problem on a compact Riemann surface
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item