Displaying similar documents to “Injectivity onto a star-shaped set for local homeomorphisms in n-space”

A note on the Cahn-Hilliard equation in H 1 ( ℝ N ) involving critical exponent

Jan W. Cholewa, Aníbal Rodríguez-Bernal (2014)

Mathematica Bohemica

Similarity:

We consider the Cahn-Hilliard equation in H 1 ( ℝ N ) with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as | u | → ∞ and logistic type nonlinearities. In both situations we prove the H 2 ( ℝ N ) -bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J. W. Cholewa, A. Rodriguez-Bernal (2012).

Retractions onto the Space of Continuous Divergence-free Vector Fields

Philippe Bouafia (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We prove that there does not exist a uniformly continuous retraction from the space of continuous vector fields onto the subspace of vector fields whose divergence vanishes in the distributional sense. We then generalise this result using the concept of m -charges, introduced by De Pauw, Moonens, and Pfeffer: on any subset X ⊆ ℝ n satisfying a mild geometric condition, there is no uniformly continuous representation operator for m -charges in X .