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pro vyhledávání: '"26b25"'
Autor:
Mussnig, Fabian, Ulivelli, Jacopo
We show that analytic analogs of Brunn-Minkowski-type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and by connecting the problem to results of Colesanti, Hug, and Saor\'in G
Externí odkaz:
http://arxiv.org/abs/2412.05001
We study concavity properties of positive solutions to the Logarithmic Schr\"odinger equation $-\Delta u=u\, \log u^2$ in a general convex domain with Dirichlet conditions. To this aim, we analyse the auxiliary Lane-Emden problems $-\Delta u = \sigma
Externí odkaz:
http://arxiv.org/abs/2411.01614
We calculate the first order variation of the Riesz $\alpha$-energy of a log-concave function $f$ with respect to the Asplund sum. Such a variational formula induces the Riesz $\alpha$-energy measure of log-concave function $f$, which will be denoted
Externí odkaz:
http://arxiv.org/abs/2408.16141
Autor:
Knoerr, Jonas, Ulivelli, Jacopo
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the support of
Externí odkaz:
http://arxiv.org/abs/2408.06946
Autor:
Knoerr, Jonas
Valuations on the space of finite-valued convex functions on $\mathbb{C}^n$ that are continuous, dually epi-translation invariant, as well as $\mathrm{U}(n)$-invariant are completely classified. It is shown that the space of these valuations decompos
Externí odkaz:
http://arxiv.org/abs/2408.01352
Autor:
Hofstätter, Georg C., Knoerr, Jonas
We classify all continuous valuations on the space of finite convex functions with values in the same space which are dually epi-translation-invariant and equi- resp. contravariant with respect to volume-preserving linear maps. We thereby identify th
Externí odkaz:
http://arxiv.org/abs/2407.08304
Autor:
Gallo, Marco, Squassina, Marco
In this paper we study convexity properties for quasilinear Lane-Emden-Fowler equations of the type $$ \begin{cases} -\Delta_p u = a(x) u^q & \quad \hbox{ in $\Omega$},\\ u >0 & \quad \hbox{ in $\Omega$}, \\ u =0 & \quad \hbox{ on $\partial \Omega$},
Externí odkaz:
http://arxiv.org/abs/2405.05404
Level proximal subdifferential was introduced by Rockafellar recently as a tool for studying proximal mappings of possibly nonconvex functions. In this paper we give a systematic study of level proximal subdifferntial, characterize variational convex
Externí odkaz:
http://arxiv.org/abs/2406.00648
Recently, the so-called Hermite-Hadamard inequality for (operator) convex functions with one variable has known extensive several developments by virtue of its nice properties and various applications. The fundamental target of this paper is to inves
Externí odkaz:
http://arxiv.org/abs/2405.12251
Autor:
Ivanov, Vsevolod I.
In this paper, we obtain a new proof of Fritz John necessary optimality conditions for vector problems applying Kakutani fixed point theorem and Hadamard directional derivative. We also derive a similar proof of second-order Fritz John necessary opti
Externí odkaz:
http://arxiv.org/abs/2405.11593