https://mathematicalanalysis.unibo.it/issue/feedBruno Pini Mathematical Analysis Seminar2019-02-06T09:47:58+01:00Annamaria Montanariannamaria.montanari@unibo.itOpen Journal Systems<strong>Bruno Pini Mathematical Analysis Seminar (BPMAS) – ISSN 2240-2829</strong> publishes seminars solicited by the Department of Mathematics, University of Bologna. It features recent developments in mathematical analysis.https://mathematicalanalysis.unibo.it/article/view/8939<em>W</em><sup>2,p</sup> a priori estimates for nonvariational operators: the sharp maximal function technique2019-02-06T09:47:51+01:00Marco Bramantimarco.bramanti@polimi.it<p>We consider a nonvariational degenerate elliptic operator, structured on a system of left invariant, 1-homogeneous, Hörmander vector fields on a Carnot group, where the coefficient matrix is symmetric, uniformly positive on a bounded domain and the coefficients are locally VMO. We discuss a new proof (given in [BT] and also based on results in [BF]) of the interior estimates in Sobolev spaces, first proved in [BB-To]. The present proof extends to this context Krylov' technique, introduced in [K1], consisting in estimating the sharp maximal function of second order derivatives.</p><p> </p>2018-12-31T00:00:00+01:00Copyright (c) 2018 Marco Bramantihttps://mathematicalanalysis.unibo.it/article/view/8942Local boundedness of vectorial minimizers of non-convex functionals2019-02-06T09:47:53+01:00Giovanni Cupinigiovanni.cupini@unibo.itMatteo Focardimatteo.focardi@unifi.itFrancesco Leonettileonetti@univaq.itElvira Mascolomascolo@math.unifi.itWe prove a local boundedness result for local minimizers of a class of non-convex functionals, under special structure assumptions on the energy density. The proof follows the lines of that in [CupLeoMas17], where a similar result is proved under slightly stronger assumptions on the energy density.2018-12-31T00:00:00+01:00Copyright (c) 2018 Giovanni Cupini, Matteo Focardi, Francesco Leonetti, Elvira Mascolohttps://mathematicalanalysis.unibo.it/article/view/8944The method of moving planes: a quantitative approach2019-02-06T09:47:54+01:00Giulio Ciraologiulio.ciraolo@unipa.itAlberto Roncoronialberto.roncoroni01@universitadipavia.itWe review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some recent results related to quantitative studies of the method of moving planes, where quantitative approximate symmetry results are obtained.2018-12-31T00:00:00+01:00Copyright (c) 2018 Giulio Ciraolo, Alberto Roncoronihttps://mathematicalanalysis.unibo.it/article/view/8945On principal frequencies and inradius in convex sets2019-02-06T09:47:55+01:00Lorenzo Brascolorenzo.brasco@unife.itWe generalize to the case of the p-Laplacian an old result by Hersch and Protter. Namely, we show that it is possible to estimate from below the first eigenvalue of the Dirichlet p-Laplacian of a convex set in terms of its inradius. We also prove a lower bound in terms of isoperimetric ratios and we briefly discuss the more general case of Poincarè-Sobolev embedding constants. Eventually, we highlight an open problem.2018-12-31T00:00:00+01:00Copyright (c) 2018 Lorenzo Brascohttps://mathematicalanalysis.unibo.it/article/view/8948Critical exponents and where to find them2019-02-06T09:47:56+01:00Sandra Lucentesandra.lucente@uniba.itIn this expository paper we present a list of different semilinear wave-type problems with time-variable coefficients. The aim of this work is to understand the influence of such coefficients on the critical exponents for polynomial nonlinearities. Statements of global existence and blow-up will follow according to exponents which are below or above these critical ones.2018-12-31T00:00:00+01:00Copyright (c) 2018 Sandra Lucentehttps://mathematicalanalysis.unibo.it/article/view/8963Some Remarks on Pohozaev-Type Identities2019-02-06T09:47:57+01:00Francesca Da Liofdalio@math.ethz.ch<p>In this note we present some Pohozaev-type identities that have been recently established in a joint work with Paul Laurain and Tristan Rivière in the framework of half-harmonic maps defined either on the real line or on the unit circle with values into a closed n-dimensional manifold. Weak half-harmonic maps are defined as critical points of the so-called half Dirichlet energy.</p><p>By using the invariance of the half Dirichlet energy with respect to the trace of the Möbius transformations we derive a countable family of relations involving the Fourier coefficients of weak half-harmonic maps. We also present a short overview of Pohozaev formulas in 2-D in connection with Noether's theorem.</p>2018-12-31T00:00:00+01:00Copyright (c) 2018 Francesca Da Liohttps://mathematicalanalysis.unibo.it/article/view/8969The regularity problem for geodesics of the control distance2019-02-06T09:47:57+01:00Roberto Montimonti@math.unipd.itIn this survey, we present some recent results on the problem about the regularity of length-minimizing curves in sub-Riemannian geometry. We also sketch the possible application of some ideas coming from Geometric Measure Theory.2018-12-31T00:00:00+01:00Copyright (c) 2018 Roberto Montihttps://mathematicalanalysis.unibo.it/article/view/8991On maximal regularity for the Cauchy-Dirichlet mixed parabolic problem with fractional time derivative2019-02-06T09:47:58+01:00Davide Guidettidavide.guidetti@unibo.itIn this seminar we illustrate some results of maximal regularity for the Cauchy-Dirichlet mixed problem, with a fractional time derivative of Caputo type in spaces of continuous and Hölder continuous functions.2018-12-31T00:00:00+01:00Copyright (c) 2018 Davide Guidetti