Graduate Courses Courses Description (Selection)

MAS 603 Partial Differential Equations

First order quasi-linear equations, the method of characteristics. Classification and normal forms. Existence theorem of Cauchy- Kovalevskaya and uniqueness theorem of Holmgren. Distributions and weak solutions. Hyperbolic theory, characteristics, propagation of singularities. Wave equation in one, two and three space dimensions. Conservation laws and shock waves. Elliptic theory, Laplace and Poisson equations, fundamental solutions, harmonic functions. Variational formulation of elliptic boundary value problems. Parabolic theory, heat equation, parabolic initial/boundary value problems.

MAS 605 Elliptic Partial Differential Equations of 2nd order

Laplace equation, fundamental solutions, Green's function, maximum principle, Poisson kernel, Harmonic functions and their properties, Harnack inequalities, equations with variable coefficients, Dirichlet problem, existence and regularity of solutions. Sobolev Spaces

MAS 617 Topics in Analysis

Free Boundary problems, the thick obstacle problem, the thin obstacle problem, two phase problems, Alt-Caffarelli-Friedman monotonicity formula, Almgren’s monotonicity formula, optimal regularity in elliptic and parabolic problems.

Undergraduate Courses Description (Selection)

MAS 303 Partial Differential Equations

Separation of variables – Fourier series. First order Partial Differential Equations. Nonlinear first order Partial Differential Equations. Linear second order Partial Differential Equations. Elliptic, Parabolic and Hyperbolic Partial Differential Equations.

University of Cyprus:

Spring 2020: ΜΑΣ 605

Fall 2019: ΜΑΣ 603

Fall 2019: ΜΑΣ 303

Spring 2019: MAS 617

Fall 2018: ΜΑΣ 606