Study of poincare hardy type inequalities and eigenvalue problems for second order elliptic pdes

Abstract

The major text of this thesis is studying Poincar 233 Hardy and Hardy Rellich type inequalities on one of the most discussed Cartan Hadamard manifold namely hyperbolic space and studying eigenvalue problems for second order elliptic PDEs The thesis is divided into two parts In the first part we have centralized our attention on the following three problems 8226 On some strong Poincar 233 inequalities on Riemannian models and their improvements 8226 On higher order Poincar 233 inequalities with radial derivatives and Hardy improvements on the hyperbolic space 8226 Hardy Rellich and second order Poincar 233 identities on the hyperbolic space via Bessel pairs In the second part we have focused our essence on the following two problems 8226 Generalized principal eigenvalues of convex nonlinear elliptic operators in RN 8226 On ergodic control problem for viscous Hamilton Jacobi equations for weakly coupled elliptic systems newline newline