Research group in Geometric Elliptic Nonlinear problems
Post-docs and graduate students
Francesca De Marchis, Giusi Vaira
Elliptic problems: existence of solutions of planar problems (Liouville equation,Toda system) via perturbative methods. Problems with supercritical growth in bounded and unbounded domains. Qualitative properties: symmetry, Morse index and asymptotic behaviour of solutions.
Parabolic problems, blow-up in finite and infinite time, analysis of initial data whose corresponding solutions blow up in finite time or exist globally.
Elliptic and parabolic equations of 4th order: existence multiplicity of solutions, concentrations and qualitative properties of solutions with respect to the asymptotic behaviour of the parameters.
Anisotropic degenerate elliptic equations, fractional Laplacians, nonlocal problems, Liouville type theorems, oscillation decrease argument, distance function to the boundary of the strip, sharp trace Hardy Sobolev Mazya inequalities.
Study of compactness properties of the Yamabe problem. Qualitative properties of the Green function in symmetric domains.
Computation of multi-dimensional potentials, multi-dimensional BVP for parabolic or elliptic equations: approximation of the solution.
Fully non linear equations
Limit of validity of the Maximum Principle (including principal eigenvalues, unbounded domains, etc…) Regularity of solutions. Qualitative properties. Degenerate or singular equations. Non local approach.