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A symmetrization result for nonlinear elliptic equations.

Vincenzo Ferone, Basilio Messano (2004)

Revista Matemática Complutense

We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = g(x,u) + f, where the principal term is a Leray-Lions operator defined on W01,p (Ω). The function g(x,u) satisfies suitable growth assumptions, but no sign hypothesis on it is assumed. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.

A Two-Particle Quantum System with Zero-Range Interaction

Michele Correggi (2008/2009)

Séminaire Équations aux dérivées partielles

We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.

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