239 reputation
219
bio website linkedin.com/in/tommibrander
location Jyväskylä, Finland
age 27
visits member for 5 years, 5 months
seen 19 hours ago
Doctoral student at the University of Jyväskylä. Research interests: Calderón problem, non-linear PDE.

Mar
17
comment Fredholm integral with functions constrained to [0;1]
Crossposted to math.SE math.stackexchange.com/questions/1192779/… . Please don't post the same question to several sites at once, or at least provide a link if you do.
Mar
12
comment Harmonic functions subject to orthogonality condition
For you $\bar \Omega$ is not the closure of Omega, right?
Feb
23
comment Extension of Sobolev Functions
Suppose Omega is, say, a square or cube, and u(x) = x_n. Can you solve your problem in this or other simplified situation?
Feb
23
comment probabilistic interpretation of elliptic equation with mixed boundary condition
How much do you already know? Can you establish the probabilistic interpretation in a simpler situation, and if so, why is this more difficult?
Feb
5
comment Mountain Pass theorem for minimization problems with constraints
Linking theorem might be useful. The aforementioned references should contain relevant material.
Feb
5
comment Mountain Pass theorem for minimization problems with constraints
There are generalisations of the theorem: see for example references [17] and [24] in master's thesis of Eero Ruosteenoja: jyx.jyu.fi/dspace/handle/123456789/41049
Feb
5
awarded  Commentator
Feb
5
comment Mountain Pass theorem for minimization problems with constraints
Mountain pass theorem finds saddle points. What are you precisely looking, a minimum of the functional or a saddle point?
Feb
2
revised Space of p-harmonic functions
added a tag
Jan
31
comment Space of p-harmonic functions
@Craig I am aware of Lindqvist's notes. I don't remember them answering this sort of question, but I have not read through them in detail. Can you be more precise with the reference?
Jan
29
revised What is the limit of the derivative of the harmonic extension/Dirichlet solution in $C^{1,\alpha}$ cases?
corrected spelling
Jan
29
suggested approved edit on What is the limit of the derivative of the harmonic extension/Dirichlet solution in $C^{1,\alpha}$ cases?
Jan
29
asked Space of p-harmonic functions
Nov
25
comment Strong solution to $u_t - \Delta_p u = f$
I am not familiar with the p-heat equation, but for the stationary p-Laplace equation the best classical regularity for solutions is $C^{1,\alpha}$. The E-L equation of the energy $\int (|\nabla u|^2+\varepsilon)^{p/2}$ does hold point-wise and its solutions converge in $C^1$ to solutions of the original equation. Maybe something like this could be useful for you?
Sep
30
awarded  Explainer
Aug
15
comment inequality involving gradient of two harmonic functions
Without reading the paper in detail: If $u \geq v$ and they are equal at a boundary point, then you may have $|\nabla u| \geq |\nabla v|$ or $|\nabla u| \leq |\nabla v|$ with both $u$ and $v$ linear affine. Take $\Omega$ a circle. In the paper one of the functions is related to the capacity of set being investigated. Maybe that is relevant.
Apr
23
revised “Limited angle” in n-dimensional Radon transform?
added inverse problems tag
Apr
23
revised Partial recovery from Radon transform
corrected tagging
Apr
23
suggested approved edit on “Limited angle” in n-dimensional Radon transform?
Apr
23
suggested approved edit on Partial recovery from Radon transform