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We start by studying the finite extinction time for solutions of the abstract Cauchy problem u(t) + Au + Bu = 0 where A is a maximal monotone operator and B is a positive operator on a Hilbert space H. We use a suitable spectral energy method to[...]texto impreso
Muñoz-Fernández, Gustavo A. ; Sarantopoulos, Yannis ; Seoane-Sepúlveda, Juan B. | Heldermann Verlag | 2008Given a trinomial of the form p(x) = ax(m) + bx(n) + c with a, b, c is an element of R, we obtain, explicitly, the best possible constant M.,,(x) in the inequality vertical bar p'(x)vertical bartexto impreso
We introduce a suitable notion of asymptotic smoothness on infinite dimensional Banach spaces, and we prove that, under some structural restrictions on the space, the convex envelope of an asymptotically smooth function is asymptotically smooth.[...]texto impreso
In this paper we use some energy methods to study the location (and formation) of a free boundary arising in some unilateral problems, for instance, in the obstacle problem and the Stefan problem.texto impreso
A mapping phi : [-1, 1] -> [0, infinity) is a curved majorant for a polynomial p in one real variable if vertical bar p(x)vertical bartexto impreso
We show that if X is a Banach space whose dual X* has an equivalent locally uniformly rotund (LUR) norm, then for every open convex U subset of X, for every real number epsilon > 0, and for every continuous and convex function f : U -> R (not [...]texto impreso
We consider the problem of finding sufficient conditions for a locally Lipschitz mapping between Finsler manifolds to be a global homeomorphism. For this purpose, we develop the notion of Clarke generalized differential in this context and, usin[...]texto impreso
In this paper we study the connections between moduli of asymptotic convexity and smoothness of a Banach space, and the existence of high order differentiable bump functions or equivalent norms on the space. The existence of a high order uniform[...]texto impreso
Let (Y0, Y1) be a Banach couple and let Xj be a closed complemented subspace of Yj ; (j = 0; 1). We present several results for the general problem of finding necessary and sufficient conditions on the parameters (?, q) such that the real interp[...]texto impreso
We investigate limiting J-interpolation methods for general Banach couples, not necessarily ordered. We also show their relationship with the interpolation methods defined by the unit square.texto impreso
Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Manzano, Antonio ; Martínez, Antón | Heldermann Verlag | 2007Let A0 and A1 be quasi-Banach spaces with A0 ,! A1. By means of a direct approach, we show that the interpolation spaces on (A0;A1) generated by the function parameter tµ(1 + j log tj)¡b can be expressed in terms of classical real inter-polation[...]texto impreso
Araujo, G. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Heldermann Verlag | 2017A number of sharp inequalities are proved for the space P (2D (?/4)) of 2-homogeneous polynomials on ?2 endowed with the supremum norm on the sector D (?/4) := {ei? : ? ? [0, ?/4]}. Among the main results we can find sharp Bernstein and Markov i[...]texto impreso
Muñoz-Fernández, Gustavo A. ; Pellegrino, D. ; Seoane-Sepúlveda, Juan B. ; Weber, A. | Heldermann Verlag | 2014We consider the Banach space of two homogeneous polynomials endowed with the supremum norm parallel to . parallel to(D(beta)) over circle sectors D(beta) of angle beta for several values of beta is an element of [0, 2 pi]. We provide an explicit[...]
