A brief introduction to elliptic and parabolic regularity theory, the L^p and Schauder estimates. Nonlinear elliptic equations, variational methods, methods of upper and lower solutions, fixed point method, bifurcation method. Nonlinear parabolic equations, global existence, stability of steady states, traveling wave solutions. Conservation laws, Rankine-Hugonoit jump condition, uniqueness issue,, entropy condition, Reimann problem for Burger's equation and p-systems.pre-rec:
MATH 7530 or by instructor's approval.