The present article is devoted to the study of the well-posedness, blow-up criterion and lower semicontinuity of the existence time for the full compressible Euler equations in R , N ≥ 1. First, let π = p(γ−1)/2γ and B 2,r ↪→ C, we show that the solution v = (π, u, S) is well-posed in B 2,r to the full compressible Euler equations, provided there exists a c > 0 such that the initial data entrop...

We study weak lower semicontinuity of integral functionals in W 1,p under standard p-growth conditions, with integrands whose negative part may have p-growth as well. MSC 2000: 49J45

For every finite nonnegative measure ft we introduce the Sobolev spaces W^'(Q,K) and we study the lower semicontinuity of functionals of the form where the integrand / is quasiconvex.

We introduce a notion of upper semicontinuity, weak upper semicontinuity, and show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. We show that our result generalizes the pure strategy existence theorem of Dasgupta and Maskin [3] and that it is neither implied nor does it imply the existen...

We prove a semicontinuity theorem for an integral functional made up by a polyconvex energy and a surface term. Our result extends to the BV framework a well known result by John Ball.

We prove lower semicontinuity of the Galois groupoid a vector field depending on parameters. Apply to Painlevé equations, this result can be used compute their groupoids for general values

The concept of upper and lower semicontinuity of fuzzy mappings introduced by Bao and Wu [Y.E. Bao, C.X. Wu, Convexity and semicontinuity of fuzzy mappings, Comput. Math. Appl., 51 (2006) 1809–1816] is redefined by using the concept of parameterized triples of fuzzy numbers. On the basis of the linear ordering of fuzzy numbers proposed by Goetschel and Voxman [R. Goetschel, W. Voxman, Elementar...