We construct a degree for mappings of the form F + K between Banach spaces, where F is C1 Fredholm of index 0 and K is compact. This degree generalizes both the LeraySchauder degree when F = I andâ€¦ (More)

We present computational algorithms for the calculation of impasse points and higher-order singularities in quasi-linear differential-algebraic equations. Our method combines a reduction step,â€¦ (More)

This paper presents a general method to associate the operator splitting for the Peaceman-Rachford procedure with a decomposition of the domain in problems arising from finite element discretizationâ€¦ (More)

We investigate the relationship between the decay at infinity of the right-hand side f and solutions u of an equation Lu = f when L is a second order elliptic operator on RN . It is shown that when Lâ€¦ (More)

We consider an elementwise data-parallel finite element procedure, recently proposed by Layton and Rabier [Appl. Math. Lett., 5 (1992), pp. 67â€“70], [J. Numer. Linear Algebra Appl., 2 (1995), pp.â€¦ (More)

Given a family A(t) of closed unbounded operators on a UMD Banach space X with common domain W, we investigate various properties of the operator DA := d dt âˆ’ A(Â·) acting from W per := {u âˆˆ W (0, 2Ï€;â€¦ (More)

Over centuries people have been fascinated by the problem of how to determine the motion of systems of rigid bodies or mass points that are subject to external forces and constraints. Today theâ€¦ (More)

Let v be a distribution on RN with gradient in Lp for some 1 â‰¤ p <âˆž and let Î³ âˆˆ (0, 1) if p â‰¤ N, Î³ âˆˆ [1âˆ’N/p, 1) if p > N. The main result of this paper states that if |x|(1âˆ’Î³)pâˆ’N âˆ— |âˆ‡v|p âˆˆ Lâˆž, then vâ€¦ (More)