Weak solutions for nonlocal boundary value problems with low regularity data
The author considers the following quasilinear parabolic initial boundary value problem \[ \begin{alignedat}{2}2 u_t+ A(t,x,u)u &= f(t, x,u) \quad&&\text{in }Q_T= (0,T)\times \Omega,\\ B(t,x,u)u &= k(t,x,u) \quad&&\text{on }\partial\Omega,\\ u(x,) &= u_0(x) \quad&&\text{in }\Omega, \end{alignedat} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^d\) \((d\geq 2)\), \(A(t,x,u)\) is strongly elliptic, and the boundary operator \(B\) is nonlocal. The goal of the author is to study weak (or very weak) solutions of the corresponding stationary and evolution problem related to the equations above. To this end the author uses maximal regularity.
scientific article; zbMATH DE number 5152782
scientific article