Boundary behavior and interior Hölder regularity of solution to nonlinear stochastic partial differential equations driven by space-time white noise

Beom-seok Han, Kyeong-hun Kim

We present uniqueness and existence in weighted Sobolev spaces of the equation $$u_t=(a{u}_{xx}+b{u}_x+cu)+\xi |u{|}^{1+\lambda }\dot{B},t>0,x\in (0,1)$$ with initial data $u(…