On the Hölder property for functions from the class \(B_{q,s}\)
For \(\Omega\) a bounded open set in \(\mathbb{R}^n\), the author introduces a class \(B_{q, s}\) of functions \(u(x, t)\), \(x\in \Omega\), \(t\in (0, T)\) containing generalized solutions of some higher order quasilinear parabolic equations, and proves that \(B_{q, s}\) is imbedded into the space of Hölder functions. The class \(B_{q, s}\) is a subspace of \(C(0, T; L_2(\Omega))\cap L_q(0, T; W^1_q(\Omega))\) and extends the spaces \(B_2\) and \(B_q\) defined earlier by Ladyzhenskaya, Solonnikov, Uralceva \((B_2= B_{2,1})\) and Di Benedetto \((B_q= B_{q, 1})\).
generalized solutions of some higher order quasilinear parabolic equations
scientific article; zbMATH DE number 652283