340 reputation
113
bio website
location Brazil
age 26
visits member for 1 year, 11 months
seen Aug 25 at 20:35

My name is José Carlos. I am doctors student and my main study is partial differential equations.


Aug
22
awarded  Critic
Aug
21
awarded  Supporter
Jul
14
revised Question about a particular estimate in Riemannian geometry.
added 1925 characters in body
Jul
12
asked Question about a particular estimate in Riemannian geometry.
Jul
2
awarded  Curious
May
19
comment Consequence of elliptic estimates up to the boundary
Let me answer your questions. By the supremum definition, there exists a sequence $(y^j)_j$ such that $u(y^{j})\rightarrow M$, therefore you have no hypothesis about the behavior of this sequence and you have no hypothesis about the behavior of the solution $u$ at the infinity, you have only a solution of this problem. The "t-finite interval" means that for each subset $[0,t]\subset[0,\infty]$, the function $f$ is Lipschitz in $u$ on $[0,M]$. My doubt can be found in the Lemma $1$ of the paper "Symmetry for elliptic equations in a half space - Berestycki, Caffarelli, Nirenberg".
May
18
asked Consequence of elliptic estimates up to the boundary
May
8
asked Gradient elliptic estimate.
Apr
26
accepted Uniform convergence in the Poisson equation…
Apr
26
comment Method of Moving Planes and Method of Moving Spheres
We can find some results about symmetry in unbounded domains using the method of moving planes (H. Berestycki, L.A. Caffarelli and L. Nirenberg-Symmetry for elliptic equations in a half space). In this case, how could I decide which method to use?
Jan
27
comment Laplacian identity.
Thank you very much for help me.
Jan
27
comment Laplacian identity.
Elegant solution. Thank you very much!
Jan
27
accepted Laplacian identity.
Jan
27
comment Laplacian identity.
We have a general product rule for the Laplacian: $$\Delta(f.g)=f\Delta g+2\nabla f.\nabla g+g\Delta f.$$
Jan
27
revised Laplacian identity.
added 22 characters in body
Jan
27
comment Laplacian identity.
I read that this is a general identity! $f$ and $g$ would be $C^\infty$ functions.
Jan
27
asked Laplacian identity.
Oct
1
awarded  Yearling
Jun
17
comment Proving unique weak solution.
Thank you for this observations. You are right. I knew that the proof of this inequality is non-trivial, but as I dont know to prove this, I wrote just what I did in my exercise.
Jun
16
answered Proving unique weak solution.