Topics in elliptic problems: from semilinear equations to shape optimization
Topics in elliptic problems: from semilinear equations to shape optimization
In this paper, which corresponds to an updated version of the author's Habilitation lecture in Mathematics, we do an overview of several topics in elliptic problems. We review some old and new results regarding the Lane-Emden equation, both under Dirichlet and Neumann boundary conditions, then focus on sign-changing solutions for …