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Authors:
Laurent Saloff-Coste; Tianyi Zheng Abstract: Laurent Saloff-Coste, Tianyi ZhengWe study the isoperimetric profiles of certain families of finitely generated groups defined via marked Schreier graphs and permutation wreath products. The groups we study are among the “simplest” examples within a much larger class of groups, all defined via marked Schreier graphs and/or action on rooted trees, which includes such examples as the long (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Panki Kim; Renming Song, Zoran Vondraček Abstract: Panki Kim, Renming Song, Zoran VondračekIn this paper we study the Martin boundary at infinity for a large class of purely discontinuous Feller processes in metric measure spaces. We show that if $\infty$ is accessible from an open set $D$, then there is only one Martin boundary point of $D$ associated with it, and this point is minimal. We also prove the analogous result for finite (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
José Bonet; Jari Taskinen Abstract: José Bonet, Jari TaskinenGiven a continuous, radial, rapidly decreasing weight $v$ on the complex plane, we study the solid hull of its associated weighted space $H_v^\infty(\mathbb C)$ of all the entire functions $f$ such that $v f $ is bounded. The solid hull is found for a large class of weights satisfying the condition (B) of Lusky. Precise formulations are obtained for weights of the (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Giovany Figueiredo; Antonio Suárez Abstract: Giovany Figueiredo, Antonio SuárezIn this paper we study the validity of the comparison principle and the sub-supersolution method for Kirchhoff type equations. We show that these principles do not work when the Kirchhoff function is increasing, contradicting some previous results. We give an alternative sub-supersolution method and apply it to some models. PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Hyeonbae Kang; Mihai Putinar Abstract: Hyeonbae Kang, Mihai PutinarA generalization of a classical argument of Mark G. Krein leads us to the conclusion that the Neumann–Poincar´e operator associated to the Lamé system of linear elastostatics equations in two dimensions has the same spectrum on the Lebesgue space of the boundary as the more natural energy space. A similar result for the Neumann–Poincaré operator associated (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Antonio Jiménez-Vargas
Abstract: Antonio Jiménez-VargasLet $X$ be a pointed metric space and let Lip$_0(X)$ be the space of all scalar-valued Lipschitz functions on $X$ which vanish at the base point. We prove that Lip$_0(X)$ with the bounded weak* topology $\tau_{bw^*}$ has the approximation property if and only if the Lipschitz-free Banach space $\mathcal F(X)$ has the approximation property if and only if, for each (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Giacomo Cherubini; Morten Risager Abstract: Giacomo Cherubini, Morten RisagerLet $e(s)$ be the error term of the hyperbolic circle problem, and denote by $e_\alpha(s)$ the fractional integral to order $\alpha$ of $e(s)$. We prove that for any small $\alpha>0$ the asymptotic variance of $e_\alpha(s)$ is finite, and given by an explicit expression. Moreover, we prove that $e_\alpha(s)$ has a limiting distribution. PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Janna Lierl
Abstract: Janna LierlThis paper proves the strong parabolic Harnack inequality for local weak solutions to the heat equation associated with time-dependent (nonsymmetric) bilinear forms. The underlying metric measure Dirichlet space is assumed to satisfy the volume doubling condition, the strong Poincaré inequality, and a cutoff Sobolev inequality. The metric is not required to be geodesic. Further (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Emanuel Carneiro; Renan Finder, Mateus Sousa Abstract: Emanuel Carneiro, Renan Finder, Mateus SousaIn this paper we establish that several maximal operators of convolution type, associated to elliptic and parabolic equations, are variation-diminishing. Our study considers maximal operators on the Euclidean space $\mathbb R^d$, on the torus $\mathbb T^d$ and on the sphere $\mathbb S^d$. The crucial regularity property that these maximal (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Martin Dindoš; Sukjung Hwang Abstract: Martin Dindoš, Sukjung HwangWe establish $L^p$, $2\le p\le\infty$, solvability of the Dirichlet~boundary value problem for a parabolic equation $u_t- \mathrm {div}(A\nabla u) - \boldsymbol{B}\cdot\nabla u =0$ on time-varying domains with coefficient matrices $A=[a_{ij}]$ and $\boldsymbol{B} = [b_{i}]$ that satisfy a small Carleson condition. The results are sharp in the following sense. (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Erlan Nursultanov; Sergey Tikhonov, Nazerke Tleukhanova Abstract: Erlan Nursultanov, Sergey Tikhonov, Nazerke TleukhanovaWe obtain upper and similar lower estimates of the ($L_p, L_q$) norm for the convolution operator. The upper estimate improves on known convolution inequalities. The technique to obtain lower estimates is applied to study boundedness problems for oscillatory integrals. PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Francisco Javier Turiel; Antonio Viruel Abstract: Francisco Javier Turiel, Antonio ViruelConsider a smooth effective action of a torus $\mathbb T^n$ on a connected $C^{\infty}$-manifold $M$. Assume that $M$ is not a torus endowed with the natural action. Then we prove that there exists a complete vector field $X$ on $M$ such that the automorphism group of $X$ equals $\mathbb T^n \times \mathbb R$, where the factor $\mathbb R$ comes from (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Luis Barreira; Jinjun Li, Claudia Valls Abstract: Luis Barreira, Jinjun Li, Claudia VallsFor expansive continuous maps with the specification property, we compute the topological entropy of the irregular set for the Birkhoff averages of a continuous function. This is the set of points for which the Birkhoff averages do not converge. The entropy is expressed in terms of a conditional variational principle. We also consider the general case (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
David Alonso; Jesús Bastero Abstract: David Alonso, Jesús BasteroWe show that for any $1\leq p\leq\infty$, the family of random vectors uniformly distributed on hyperplane projections of the unit ball of $\ell_p^n$ verify the variance conjecture$$\mathrm {Var} X ^2 \leq C \mathrm {max}_{\xi\in S^{n-1}}\mathbb E\langle X,\xi\rangle^2\, \mathbb E X ^2,$$where $C$ depends on $p$ but not on the dimension $n$ or the (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Maurizio Cailotto; Luisa Fiorot Abstract: Maurizio Cailotto, Luisa FiorotThis paper is devoted to the comparison of the notions of regularity for algebraic connections and regularity for (holonomic) algebraic $\mathcal D$-modules. PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Marco Magliaro; Luciano Mari, Marco Rigoli Abstract: Marco Magliaro, Luciano Mari, Marco RigoliThe aim of this paper is to study a new equivalent form of the weak maximum principle for a large class of differential operators on Riemannian manifolds. This new form has been inspired by the work of Berestycki, Hamel and Rossi for trace operators, and allows us to shed new light on it and to introduce a new sufficient bounded Khas’minskii type (...) PubDate: Mon, 28 May 2018 23:30:02 +020

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Authors:
Steffen Rohde; Huy Tran, Michel Zinsmeister Abstract: Steffen Rohde, Huy Tran, Michel ZinsmeisterThe proofs of continuity of Loewner traces in the stochastic and in the deterministic settings employ different techniques. In the former setting of the Schramm–Loewner evolution SLE, H¨older continuity of the conformal maps is shown by estimating the derivatives, whereas the latter setting uses the theory of quasiconformal maps. In this note, (...) PubDate: Mon, 28 May 2018 23:30:02 +020