15 Dicembre, 2009 16:15 in punto

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Hardy-Rellich type inequalities with boundary terms and applications.

Elvise Berchio, Politecnico di Milano

aula seminari III piano

We present a family of Hardy-Rellich type inequalities having boundary terms and where the optimal constants are not necessarily the classical Hardy-Rellich ones. When the domain is the unit ball the exact values of the constants are performed. We exploit this fact to study the regularity of the “extremal solution” to some semilinear elliptic problems under Steklov boundary conditions.