Blogs about: Pdes
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Cofactor matrix has divergence-free rows
In this entry, we prove the following interesting result Let be a smooth function. Then for each fixed. For simplicity, let us write . Then Proof. We recall from this entry that for each matrix , This… more →
Quốc Anh Ngô
Definition of coercivity
wrote 1 year ago: This is a classical question: how could we understand the coercivity of the operator ? Given a smoot … more →
Stereographic projection, 4
wrote 1 year ago: It turns out that, via the stereographic projection, equation on with becomes with the following pro … more →
Energy functionals associate to integrals of exponential type
wrote 1 year ago: The purpose of this note is to derive some integral functionals associated to the following in the w … more →
The Yamabe problem: A Story
wrote 1 year ago: I want to write a short survey about the Yamabe problem. Long time ago, I introduced the problem in … more →
A note on the equation involving the prescribing Gaussian curvature problem, 2
wrote 1 year ago: Followed by this note, the trick use in that note also works for the following equation In fact, by … more →
The Entropy-Logarithmic energy inequality
wrote 1 year ago: Recently, I have read a result by J. Demange published in J. Funct. Anal. in 2008 [here]. In that pa … more →
Uniformly boundedness of positive smooth solutions to the Lichnerowicz equation in R^n
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wrote 1 year ago: Let us consider the following so-called Lichnerowicz equation in Recently, Brezis [here] proved the … more →
The Ekeland variational principle
wrote 2 years ago: In mathematical analysis, Ekeland’s variational principle, discovered by Ivar Ekeland, is a th … more →
Some properties of the Yamabe equation in the null case
wrote 2 years ago: Let us consider the Yamabe equation in the null case, that is where is a compact manifold of dimensi … more →
The Nehari manifold
wrote 2 years ago: In the calculus of variations, a branch of mathematics, a Nehari manifold is a manifold of functions … more →
On the uniqueness for the Yamabe problem
wrote 2 years ago: The Yamabe problem has been discussed here. Basically, starting from a metric , for a given constant … more →
On the foundations of computational mathematics
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wrote 2 years ago: Any narrow mathematical area cannot explicitly describe computational mathematics; it has all facets … more →
Method of moving planes: The cylindrically symmetric of solutions of critical Hardy–Sobolev operators
wrote 2 years ago: Recently, I have read a paper entitled “Classification of solutions of a critical Hardy-Sobole … more →
The Picone identity for p-Laplacian
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wrote 2 years ago: Last time we discussed the Picone identity for general purpose [here]. Now we present a generalizati … more →
Weak comparison principle: p-Laplacian with Neumann boundary condition
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wrote 2 years ago: I am going to summarize some known comparison principles. I will start with a weak comparison princi … more →
The (original) Picone identity
wrote 2 years ago: For differentiable functions and , the following Picone’s identity is well known The proof is … more →
Cofactor matrix has divergence-free rows
wrote 2 years ago: In this entry, we prove the following interesting result Let be a smooth function. Then for each fix … more →
Cofactor matrix has divergence-free rows
wrote 2 years ago: In this entry, we prove the following interesting result Let be a smooth function. Then for each fix … more →
log K is harmonic implies that K is contant
wrote 2 years ago: In this short note we present a result in a paper due to Edward M. Fan [here]. To be precise, we pro … more →
