Partial Differential Equations II

Learn modern theory of partial differential equations (PDEs) with emphasis on linear and nonlinear PDEs arising in various applications such as mathematical physics, fluid mechanics, mathematical biology and economics. Explore topics including Sobolev spaces and their properties, second order elliptic, parabolic and hyperbolic PDEs, concept of weak differentiability, weak solutions, Lax-Milgram theorem, energy estimates, regularity theory, Harnack inequalities, topics on nonlinear PDEs.