#### Definition of coercivity

: This is a classical question: how could we understand the coercivity of the operator ? Given a smoot … more →

#### Stereographic projection, 4

: 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

: The purpose of this note is to derive some integral functionals associated to the following in the w … more →

#### The Yamabe problem: A Story

: 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

: Followed by this note, the trick use in that note also works for the following equation In fact, by … more →

Tags: Riemannian Geometry

#### The Entropy-Logarithmic energy inequality

: 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 — 5 comments

: Let us consider the following so-called Lichnerowicz equation in Recently, Brezis [here] proved the … more →

#### The Ekeland variational principle

: 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

: Let us consider the Yamabe equation in the null case, that is where is a compact manifold of dimensi … more →

Tags: Yamabe problem

#### The Nehari manifold

: 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

: The Yamabe problem has been discussed here. Basically, starting from a metric , for a given constant … more →

Tags: Yamabe problem

#### On the foundations of computational mathematics — 1 comment

: 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

: Recently, I have read a paper entitled “Classification of solutions of a critical Hardy-Sobole … more →

Tags: Moving planes

#### The Picone identity for p-Laplacian — 1 comment

: Last time we discussed the Picone identity for general purpose [here]. Now we present a generalizati … more →

Tags: Picone identity

#### Weak comparison principle: p-Laplacian with Neumann boundary condition — 1 comment

: I am going to summarize some known comparison principles. I will start with a weak comparison princi … more →

Tags: comparison principle

#### The (original) Picone identity

: For differentiable functions and , the following Picone’s identity is well known The proof is … more →

Tags: Picone identity

#### Cofactor matrix has divergence-free rows

: 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

: 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

: In this short note we present a result in a paper due to Edward M. Fan [here]. To be precise, we pro … more →

All →