Since there are separate tags for a) ODEs, ca.classical-analysis-and-odes and differential-equations and for b) ap.analysis-of-pdes but only one tag for stochastic-differential-equations, I was wondering if it is worth creating a new tag called "stochastic partial differential equations". This is...

The following general definition of subharmonic function comes from the classical text book [elliptic partial differential equations of second order] by Gilbarg and Trudinger. We call a function $u$ subharmonic in $\Omega$ if $u \in C^0(\Omega)$ and for every ball $B \subset \subset \Omega$ and ...

In fact a weaker version of Aleksandrov's theorem is true for subharmonic functions. Since $\Delta u$ is a Radon measure, the following result follows from Proposition 4.4 in 1. Theorem. If $u:\Omega\to\mathbb{R}$ is subharmonic and locally integrable, then for almost all $x\in\Omega$ there exis...

There are some integrals related to the celebrated pair correlation conjecture of H. L. Montgomery. One of them is the integral introduced by Selberg related to estimating the variance of primes in short intervals: I read the last interesting paper of Yitang Zhang and it seems to me that the pap...