Hölder estimates of solutions to a degenerate diffusion equation (Q2781291)

There is studied the Hölder regularity of weak solutions of the Cauchy problem for the general degenerate parabolic equations NEWLINE\[NEWLINE u_t=\Delta G(u) +\sum_{j=1}^N f_j(u)_{x_j} +h(u), NEWLINE\]NEWLINE with the initial data \(u(x,0)=u_0(x_1,x_2,...,x_N),\) where the diffusion function \(G(u)\) can be a constant on a nonzero measure set, such as the equations of two-phase Stefan type. Some explicit Hölder exponents of the composition function \(G(u)\) with respect to the space variables are obtained by using the maximum principle.