I) We consider a system governed by a free boundary problem with Tresca condition on a part of the boundary of a material domain with a source term g through a parabolic variational inequality of the second kind. We prove the existence and uniqueness results to a family of distributed optimal control problems over g for each parameter h > 0, associated to the Newton law (Robin boundary conditio...

We give a proof of the “five gradients inequality” Optimal Transportation Theory for general costs form c(x,y)=h(x-y) where h is C 1 strictly convex radially symmetric function.

We prove the following generalization of the Entropy Power Inequality: h(Ax) h(A~ x) where h() denotes (joint-) diierential-entropy, x = x 1 : : : x n is a random vector with independent components, ~ x = ~ x 1 : : : ~ x n is a Gaussian vector with independent components such that h(~ x i) = h(x i), i = 1 : : : n, and A is any matrix. This generalization of the entropy-power inequality is appli...

In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type via new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, identity for differentiable convex functions of first order is proved. Then, taking into account as an auxiliary result assistance Hölder, power-mean, Young, Jensen inequality, some estimations...

Operator-valued multivariable Bohr type inequalities are obtained for: (i) a class of noncommutative holomorphic functions on the open unit ball of B(H)n, generalizing the analytic functions on the open unit disc; (ii) the noncommutative disc algebra An and the noncommutative analytic Toeplitz algebra F∞ n ; (iii) a class of noncommutative selfadjoint harmonic functions on the open unit ball of...

1. Harmonic analysis on H 2. Meromorphic continuation up to the critical line 3. Sobolev inequality/imbedding 4. Eventually-vanishing constant terms 5. Compactness of Sob(Γ\H)a → L(Γ\H) 6. Discreteness of cuspforms 7. Meromorphic continuation beyond the critical line 8. Discrete decomposition of truncated Eisenstein series 9. Appendix: Friedrichs extensions 10. Appendix: simplest Maass-Selberg ...