Relation between the boundary point spectrum of a generator and of its adjoint

In this paper we get some relations between the boundary point spectrum of the generator A of a C0-semigroup and the generator A* of the dual semigroup. These relations combined with the results due to Lyubich-Phóng and Arendt-Batty, yield stability results on positive Cosemigroup

Una clase de espacios de sucesiones vectoriales

In this paper we study certain barrelledness properties of a classe of spaces of vector sequences. This spaces, introduced by Valdivia, extend the example of a Banach quasi-reflexive space due to James

Relation between the boundary point spectrum of a generator and of its adjoint

In this paper we get some relations between the boundary point spectrum of the generator A of a C0-semigroup and the generator A* of the dual semigroup. These relations combined with the results due to Lyubich-Phóng and Arendt-Batty, yield stability results on positive Cosemigroup

A Parabolic quasilinear problem for linear growth functionals

We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth. A typical example of energy functional we consider is the one given by the nonparametric area integrand f(x,ξ)=√1+∥ξ∥2, which corresponds with the time-dependent minimal surface equation. We also study the asymptotic behaviour of the solutions.The first and third authors have been partially supported by the Spanish DGICYT, Project PB98-1442. The second author acknowledges partial support by the TMR European Project “Viscosity Solutions and their Applications”, reference FMRX-CT98-0234 and the PNPGC, Project BFM 2000-0962-C02-01

Bounded solutions to the 1-Laplacian equation with a critical gradient term

In this paper, we study the Dirichlet problem for an elliptic equation, in which the 1-Laplacian operator and lower-order terms appear. We introduce a suitable definition of solution and prove the existence of, at least, one bounded solution in BV(ohm) having a negligible jump part. Moreover, a uniqueness result for small positive data is proved, and explicit examples of solutions are shown