user avatar
user avatar
user avatar
TeenFromAlishan
  • Member for 8 months
  • Last seen this week
  • Shanghai, China
4 votes
0 answers
178 views

Problems arising from the Trudinger's paper in 1968 "Remarks concerning the conformal deformation of riemannian structures on compact manifolds"

3 votes
1 answer
189 views

A problem of using Schauder estimate in the paper of Yau's proof of calabi conjecture

2 votes
0 answers
243 views

A regularity result for semilinear PDE of the form $\Delta u=f(x, u)$ in Michael E. Taylor's book "Partial Differential Equations III"

2 votes
1 answer
143 views

Are there any researches on Liouville's equation $\Delta u=K e^{ u}$ when $K<0$?

2 votes
0 answers
79 views

Existing work on $\Delta u=c-h e^{u}$ on compact manifold with dimension n, I have read J.Kazdan's work, the condition $c > 0, n \ge 3$ is not solved

2 votes
0 answers
50 views

Question about the second order linear elliptic PDE on closed manifold

1 vote
0 answers
37 views

Question about higher order mean field equation $\left(-\Delta_{g}\right)^{m} u+\lambda=\lambda \frac{e^{2 m u}}{\int_{M} e^{2 m u} d \mu_{g}}$

1 vote
1 answer
75 views

What is $\left\| u \right\|_{ H_{0}^{k}, H_{0}^{k}}$ norm when $H_{0}^{k}=\left\{u \in H^{k, 2}(M) \mid \int_{M} u \operatorname{vol}_{g}=0\right\}$

1 vote
0 answers
107 views

A problem about using the moving plane method to prove radial symmetry of the $C^{2}$ global solution of a elliptic PDE in $R^{2}$

1 vote
0 answers
74 views

Existence of $C^{2, \alpha}$ solution to $a^{ij}(x,u,Du)D_{ij}u+b(x,u,Du)=0$ using the Leray–Schauder theorem in "Elliptic PDE" of Q. Han & F. Lin

1 vote
0 answers
41 views

Can we find a uniform bound of the solution of a series of linear partial differential equations related to a parameter

1 vote
0 answers
108 views

Problems arising from a paper on the radial symmetry of the global solution of semilinear PDE $\Delta u+f(u)=0$ in $\Bbb{R}^{n}$

1 vote
1 answer
198 views

A problem of the volume form of Kähler manifold in the paper of Yau's proof of Calabi conjecture

1 vote
1 answer
234 views

A problem arising from reading a lecture on the Yamabe problem of how the Hölder inequality is used

0 votes
1 answer
120 views

A proof for the existence of smooth solution of PDE in form $\Delta u=f(x, u)$ in Michael E. Taylor's book Partial Differential Equations III

0 votes
0 answers
48 views

Problems about Chern-Yamabe flow