Bruno Pini Mathematical Analysis Seminar
https://mathematicalanalysis.unibo.it/
<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.Dipartimento di Matematica, Università di Bolognaen-USBruno Pini Mathematical Analysis Seminar2240-2829<p>Copyrights and publishing rights of all the texts on this journal belong to the respective authors without restrictions.</p><div><a href="http://creativecommons.org/licenses/by/3.0/" rel="license"><img src="https://i.creativecommons.org/l/by/3.0/88x31.png" alt="Creative Commons License" /></a></div><p>This journal is licensed under a <a href="http://creativecommons.org/licenses/by/3.0/" rel="license">Creative Commons Attribution 3.0 Unported License</a>. (<a href="http://creativecommons.org/licenses/by/3.0/legalcode">full legal code</a>) <br />See also our <a href="/about/editorialPolicies#openAccessPolicy">Open Access Policy</a>.</p><em>W</em><sup>2,p</sup> a priori estimates for nonvariational operators: the sharp maximal function technique
https://mathematicalanalysis.unibo.it/article/view/8939
<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>Marco Bramanti
Copyright (c) 2018 Marco Bramanti
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2018-12-312018-12-319111910.6092/issn.2240-2829/8939Local boundedness of vectorial minimizers of non-convex functionals
https://mathematicalanalysis.unibo.it/article/view/8942
We 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.Giovanni CupiniMatteo FocardiFrancesco LeonettiElvira Mascolo
Copyright (c) 2018 Giovanni Cupini, Matteo Focardi, Francesco Leonetti, Elvira Mascolo
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2018-12-312018-12-3191204010.6092/issn.2240-2829/8942The method of moving planes: a quantitative approach
https://mathematicalanalysis.unibo.it/article/view/8944
We 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.Giulio CiraoloAlberto Roncoroni
Copyright (c) 2018 Giulio Ciraolo, Alberto Roncoroni
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2018-12-312018-12-3191417710.6092/issn.2240-2829/8944On principal frequencies and inradius in convex sets
https://mathematicalanalysis.unibo.it/article/view/8945
We 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.Lorenzo Brasco
Copyright (c) 2018 Lorenzo Brasco
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2018-12-312018-12-31917810110.6092/issn.2240-2829/8945Critical exponents and where to find them
https://mathematicalanalysis.unibo.it/article/view/8948
In 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.Sandra Lucente
Copyright (c) 2018 Sandra Lucente
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2018-12-312018-12-319110211410.6092/issn.2240-2829/8948Some Remarks on Pohozaev-Type Identities
https://mathematicalanalysis.unibo.it/article/view/8963
<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>Francesca Da Lio
Copyright (c) 2018 Francesca Da Lio
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2018-12-312018-12-319111513610.6092/issn.2240-2829/8963The regularity problem for geodesics of the control distance
https://mathematicalanalysis.unibo.it/article/view/8969
In 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.Roberto Monti
Copyright (c) 2018 Roberto Monti
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2018-12-312018-12-319113714610.6092/issn.2240-2829/8969On maximal regularity for the Cauchy-Dirichlet mixed parabolic problem with fractional time derivative
https://mathematicalanalysis.unibo.it/article/view/8991
In 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.Davide Guidetti
Copyright (c) 2018 Davide Guidetti
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2018-12-312018-12-319114715710.6092/issn.2240-2829/8991