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bio website math.vt.edu/people/renardym
location Blacksburg, VA
age 59
visits member for 4 years, 4 months
seen 7 hours ago

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 $\partial\Omega$.