Robert Černý (2009)
Commentationes Mathematicae Universitatis Carolinae
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We give a sufficient condition for a curve to ensure that the -dimensional Hausdorff measure restricted to is locally monotone.
Jan Mařík (1994)
Mathematica Bohemica
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A compact set is constructed such that each horizontal or vertical line intersects in at most one point while the -dimensional measure of is infinite for every .
Daniele Bartolucci, Fabiana Leoni, Luigi Orsina, Augusto C. Ponce (2005)
Annales de l'I.H.P. Analyse non linéaire
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Patrick Ballard, Stéphanie Basseville (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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A simple dynamical problem involving unilateral contact and dry friction of Coulomb type is considered as an archetype. We are concerned with the existence and uniqueness of solutions of the system with Cauchy data. In the frictionless case, it is known [Schatzman, Nonlinear Anal. Theory, Methods Appl. 2 (1978) 355–373] that pathologies of non-uniqueness can exist, even if all the data are of class . However, uniqueness is recovered provided that the data are analytic [Ballard, Arch....
Ralf Bader, Nikolaos Papageorgiou (2000)
Annales Polonici Mathematici
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We consider a quasilinear vector differential equation which involves the p-Laplacian and a maximal monotone map. The boundary conditions are nonlinear and are determined by a generally multivalued, maximal monotone map. We prove two existence theorems. The first assumes that the maximal monotone map involved is everywhere defined and in the second we drop this requirement at the expense of strengthening the growth hypothesis on the vector field. The proofs are based on the theory of...