Optimal regularity estimates for parabolic \(p\)-harmonic equations
The equation \[ u_t-\nabla\cdot(|\langle A\nabla u,\nabla u\rangle|^{{p-2\over 2}} A\nabla u)= \nabla\cdot(|\vec f|^{p-2}\vec f) \] is considered for \(p> {2n\over n+2}\), when \(A= A(x_1,\dots, x_n,t)\) is a symmetric matrix of size \(n\times n\) satisfying certain conditions. Regularity estimates are given in an Orlicz space, depending on \(\vec f\). The coefficients of the matrix \(A\) have a very small ``BMO-norm''.
scientific article; zbMATH DE number 5673242
scientific article