ﻻ يوجد ملخص باللغة العربية
We extend several known results on solvability in the Sobolev spaces $W^{1}_{p}$, $pin[2,infty)$, of SPDEs in divergence form in $bR^{d}_{+}$ to equations having coefficients which are discontinuous in the space variable.
We present several results on solvability in Sobolev spaces $W^{1}_{p}$ of SPDEs in divergence form in the whole space.
This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial differential equations (SPDEs) with locally monotone coefficients in generalized variational framework. The main result could be applied to demon
We prove that the weak version of the SPDE problem begin{align*} dV_{t}(x) & = [-mu V_{t}(x) + frac{1}{2} (sigma_{M}^{2} + sigma_{I}^{2})V_{t}(x)]dt - sigma_{M} V_{t}(x)dW^{M}_{t}, quad x > 0, V_{t}(0) &= 0 end{align*} with a specified bounded initi
We study a class of second-order degenerate linear parabolic equations in divergence form in $(-infty, T) times mathbb R^d_+$ with homogeneous Dirichlet boundary condition on $(-infty, T) times partial mathbb R^d_+$, where $mathbb R^d_+ = {x in mathb
We study a class of linear parabolic equations in divergence form with degenerate coefficients on the upper half space. Specifically, the equations are considered in $(-infty, T) times mathbb{R}^d_+$, where $mathbb{R}^d_+ = {x in mathbb{R}^d,:, x_d>0