Elliptic and Parabolic Equations - Abstract
Namlyeyeva, Yuliya
We consider wide classes of quasilinear anisotropic elliptic equations and doubly nonlinear anisotropic parabolic equations, whose solutions have singularity at a point. The model representatives of these equations are the following $$sumlimits_i=1^n left( u_x_i ^p_i-2 u_x_iright)_x_i=0,$$$$ u_t - sum^n_i=1 left( u ^(m_i-1)(p_i-1) left u_x_iright ^p_i-2 u_x_iright)_x_i = 0,$$ where $1 < p_1leqslant p_2leqslantdotsleqslant p_n.$ We establish sharp pointwise conditions for removable isolated singularity of solutions of such equations. The precise upper and lower estimates near the singularity point for solutions with non-removable point singularity are obtained.
This talk represents joint work with I.I. Skrypnik and A.E. Shishkov.