bio | website | math.vt.edu/people/renardym |
---|---|---|
location | Blacksburg, VA | |
age | 59 | |
visits | member for | 4 years, 4 months |
seen | 7 hours ago | |
stats | profile views | 3,025 |
Mar 20 |
answered | Well-posedness of Fokker-Planck equation |
Mar 16 |
reviewed | Approve Is there a characterization of Riemannian manifolds that split off two factors? |
Mar 15 |
awarded | Good Answer |
Feb 25 |
comment |
Analytic perturbation of eigenfunctions
This is true whenever eigenvalues are simple. Reference: Kato, Perturbation Theory for Linear Operators. |
Feb 23 |
comment |
Strong solution to parabolic equation without differentiability assumption on coefficient?
There is a rather extensive literature on parabolic equations with nonsmooth coefficients. The work of Ladyzhenskaya and Uraltseva is a good place to start searching. |
Feb 22 |
comment |
Multiplication of generalized functions
I realize Columbeau algebras do not address your specific question. But searching the literature on them might give you pointers to related efforts. |
Feb 22 |
comment |
Explicit formula for Bergman kernel on the unit ball
Using the convention $0^0=1$ when writing power series is fairly standard. Is that your only concern? If not, you might want to explain what $\gamma_\alpha$, $N(k)$ etc. are. |
Feb 22 |
comment |
Multiplication of generalized functions
en.wikipedia.org/wiki/Colombeau_algebra |
Feb 22 |
answered | Strong maximum principle for the heat equation in non-cylindrical domains |
Feb 21 |
comment |
Is the trivial solution the unique solution to the following initial value problem?
The linearized equation can be solved in closed form, and it does not have any nontrivial solutions for which y and y' are zero at the origin. You can probably use this as the basis for a contraction argument. |
Feb 18 |
comment |
Uniqueness of analytic center manifold
The Taylor expansion of the center manifold is unique to any order. That makes the center manifold unique in the class of analytic manifolds, if an analytic center manifold exists. |
Feb 17 |
answered | Fundamental solution to the heat equation with zero boundary values |
Feb 16 |
revised |
$n^3 | \sum_{i=1}^{n-1}\binom{n}{i}^2$ => $n | \sum_{i=1}^{n-1}\binom{n}{i}$?
added 1 character in body |
Feb 16 |
comment |
Causal (Volterra type) differential equation with local Lipschitz condition
$u^2$ does not map $L^2$ to $L^2$. But there is no need to use $L^2$ as a function space. Examine the usual existence proof for ODEs. It is based on converting the ODE to a Volterra equation! |
Feb 13 |
comment |
Oblique derivative smoothness of harmonic functions
The Cantor-Lebesgue function is Hoelder continuous, and Hilbert transform preserves Hoelder continuity. |
Feb 13 |
answered | Oblique derivative smoothness of harmonic functions |
Feb 9 |
comment |
Harmonic extension of $L^\infty$ function is in $L^\infty$?
This is just an application of the maximum principle. The Hopf lemma takes care of the Neumann boundary. |
Feb 6 |
revised |
Is it possible to get an equation with two exponentials and a bessel function in closed form?
added 11 characters in body |
Feb 4 |
comment |
Fourier-Legendre coefficients and Sobolev regularity
Your definition of $H^s$ works on the whole line, but not on an interval. Moreover, your condition on the coefficients is equivalent to $f$ being in the domain of a power of the Legendre differential operator. These domains are not the same as Sobolev spaces. |
Jan 31 |
comment |
Solution to a PDE with constant data - what is the fault in my proof?
It looks like you are missing a boundary condition on $\partial\Omega$. |