We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for finite eigenvalues are obtained by using analyticity and monotonicity properties (rather than variational principles) and they are general enough to include ...

We study connections between four different types of results that are concerned with vector-valued functions u : Ω → R of class L(Ω) on a domain Ω ⊂ R: Coercivity results in H(Ω) relying on div and curl, the Helmholtz decomposition, the construction of vector potentials, and the global div-curl lemma. Key-words: Friedrichs inquality, coercivity, div-curl lemma, compensated compactness

We prove the well-posedness of entropy weak solutions of a scalar conservation law with non-local flux arising in traffic flow modeling. The result is obtained providing accurate L∞, BV and L estimates for the sequence of approximate solutions constructed by an adapted Lax-Friedrichs scheme.