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We study the existence of everywhere differentiable functions which are almost everywhere solutions of quite general Hamilton-Jacobi equations on open subsets of R(d) or on d-dimensional manifolds whenever d > = 2. In particular, when M is a Rie[...]texto impreso
Starlike bodies are interesting in nonlinear functional analysis because they are strongly related to bump function sand to n-homogeneous polynomials on Banach spaces, and their geometrical proper ties are thus worth studying. In this paper we d[...]texto impreso
Azagra Rueda, Daniel ; Jiménez Sevilla, María del Mar ; Deville, Robert | Cambridge University Press | 2003-01We study the size of the range of the derivatives of a smooth function between Banach spaces. We establish conditions on a pair of Banach spaces X and Y to ensure the existence of a C-p smooth (Frechet smooth or a continuous G (a) over cap teaux[...]texto impreso
We investigate the best order of smoothness of L-p(L-q). We prove in particular that there exists a C-infinity-smooth bump function on L-p(L-q) if and only if p and q are even integers and p is a multiple of q.texto impreso
Two main results presented by the authors include a mean-value inequality for a class of Gateaux subdifferentiable functions and a subdifferential Rolle’s theorem in a Banach space. For the second part, if a (Gateaux/Fréchet)subdifferentiable fu[...]
