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Results tagged with ca.classical-analysis-and-odes
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user 49136
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
5
votes
On the fundamental solution for elliptic PDE
In the paper The Green Function for uniformly elliptic equations Manuscripta Mathematica Gruter & Widman proved - among other things - pointwise estimates about the gradient of the Green function unde …
2
votes
Higher integrability for Sobolev functions - part 2
I noticed derivative of volume integral is the surface one. Then $\varphi(r) = \int_{B_r}$ satisfies the differential inequality
$$
r\varphi'(r) \leq \varphi(r)
$$
You could deduce properties from tha …
3
votes
General version of Weyl's lemma
unfortunately Weyl lemma cannot be generalized to any divergence form elliptic operator. The problem is given by the smoothness of the coefficients $a_{ij}$. There is a huge literature on the subject. …