We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to maximal monotonicity, in a nonreflexive space we characterize maximality using a “enlarged” version of the duality mapping, introduced previously by Gossez....

We investigate sectoriality and maximal regularity in L-LSobolev spaces for the structurally damped plate equation with DirichletNeumann (clamped) boundary conditions. We obtain unique solutions with optimal regularity for the inhomogeneous problem in the whole space, in the half-space, and in bounded domains of class C. It turns out that the first-order system related to the scalar equation on...

In this article, the totally geodesic submanifolds in the complex 2Grassmannian G2(C) and in the quaternionic 2-Grassmannian G2(H) are classified. It turns out that for both of these spaces, the earlier classification of maximal totally geodesic submanifolds in Riemannian symmetric spaces of rank 2 published by Chen and Nagano (1978) is incomplete. For example, G2(H) with n ≥ 5 contains totally...

Born’s reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born’s theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity t...

We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation ∂tu+∆∂xu+u∂xu = 0 in the Sobolev spaces Hs(R3), s > 1, as well as in the Besov space B 2 (R 3). The proof is based on a sharp maximal function estimate in time-weighted spaces.

Confirming previous heuristic analyses à la Belinskii-Khalatnikov-Lifshitz, it is rigorously proven that certain “subcritical” Einstein-matter systems exhibit a monotone, generalized Kasner behaviour in the vicinity of a spacelike singularity. The D−dimensional coupled Einstein-dilaton-p-form system is subcritical if the dilaton couplings of the p-forms belong to some dimension dependent open n...

Inspired by the results of [APR], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and the factor power of the symmetric group. Furthermore we extend the Gelfand model for the semigroup algebr...

We will give a proof of I. G. Rosenberg’s characterization of maximal clones, first published in [11]. The theorem lists six types of relations on a finite set such that a clone over this set is maximal if and only if it contains just the functions preserving one of the relations of the list. In Universal Algebra, this translates immediately into a characterization of the finite preprimal algeb...

The classical Rubio de Francia extrapolation result asserts that if an operator T : L0(u) → Lp0,∞(u) is bounded for some p0 > 1 and every u ∈ Ap0 , then, for every 1 < p < ∞ and every u ∈ Ap, T : L(u) → Lp,∞(u) is bounded. However, there are examples showing that it is not possible to extrapolate to the end-point p = 1. In this paper we shall prove that there exists a class of weights, slightly...

This study focuses on anisotropic Sobolev type spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E, depending of α and order of spaces are found that ...