Results 21 to 30 of about 1,854 (206)

Constructions and Properties of Quasi Sigma-Algebra in Topological Measure Space

Axioms, 2022
The topological views of a measure space provide deep insights. In this paper, the sigma-set algebraic structure is extended in a Hausdorff topological space based on the locally compactable neighborhood systems without considering strictly (metrized ...
Susmit Bagchi
doaj   +1 more source

New equivalent conditions for Hardy-type inequalities [PDF]

Mathematica Bohemica
We consider a Hardy-type inequality with Oinarov's kernel in weighted Lebesgue spaces. We give new equivalent conditions for satisfying the inequality, and provide lower and upper estimates for its best constant.
Alois Kufner, Komil Kuliev, Gulchehra Kulieva, Mohlaroyim Eshimova   +3 more
doaj   +1 more source

Homoclinic solutions for a differential inclusion system involving the p(t)-Laplacian

Advances in Nonlinear Analysis, 2022
The aim of this article is to study nonlinear problem driven by the p(t)p\left(t)-Laplacian with nonsmooth potential. We establish the existence of homoclinic solutions by using variational principle for locally Lipschitz functions and the properties of ...
Cheng Jun, Chen Peng, Zhang Limin
doaj   +1 more source

A Blaschke–Lebesgue theorem for the Cheeger constant

Communications in Contemporary Mathematics, 2023
In this paper, we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal Reuleaux polygon together with an explicit upper bound for the inradius of the optimal domain.
Antoine Henrot, Ilaria Lucardesi
openaire   +2 more sources

Boundedness and Hölder continuity of weak solutions of the nonlinear boundary-value problem for elliptic equations with general nonstandard growth conditions [PDF]

Mathematica Bohemica
We study a nonlinear boundary-value problem for elliptic equations with critical growth conditions involving Lebesgue measurable functions. We prove global boundedness and Hölder continuity of weak solutions for this problem.
Gumpyong Ri, Dukman Ri
doaj   +1 more source

Szegö's Conjecture on Lebesgue Constants for Legendre Series [PDF]

Pacific Journal of Mathematics, 1988
In 1926, Szegö conjectured that the Lebesgue constants for Legendre series form a monotonically increasing sequence. In this paper, we prove that his conjecture is true. Our method is based on an asymptotic expansion together with an explicit error bound, and makes use of some recent results of Baratella and Gatteschi concerning uniform asymptotic ...
Qu, C. K., Wong, R.
openaire   +4 more sources

A goodness‐of‐fit test for regression models with discrete outcomes

Canadian Journal of Statistics, EarlyView.
Abstract Regression models are often used to analyze discrete outcomes, but classical goodness‐of‐fit tests such as those based on the deviance or Pearson's statistic can be misleading or have little power in this context. To address this issue, we propose a new test, inspired by the work of Czado et al.
Lu Yang, Christian Genest, Johanna G. Nešlehová   +2 more
wiley   +1 more source

Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and L1-Data

International Journal of Differential Equations, 2023
Nonlinear partial differential equations are considered as an essential tool for describing the behavior of many natural phenomena. The modeling of some phenomena requires to work in Sobolev spaces with constant exponent.
Ibrahime Konaté, Arouna Ouédraogo
doaj   +1 more source

Lebesgue Constants for Cantor Sets

Experimental Mathematics
We evaluate the values of the Lebesgue constants in polynomial interpolation for three types of Cantor sets. In all cases, the sequences of Lebesgue constants are not bounded. This disproves the statement by Mergelyan.
Alexander Goncharov, Yaman Paksoy
openaire   +2 more sources

Approximation of Dirac operators with δ‐shell potentials in the norm resolvent sense, II: Quantitative results

Mathematische Nachrichten, EarlyView.
Abstract This paper is devoted to the approximation of two‐ and three‐dimensional Dirac operators HV∼δΣ$H_{\widetilde{V} \delta _\Sigma }$ with combinations of electrostatic and Lorentz scalar δ$\delta$‐shell interactions in the norm resolvent sense. Relying on results from Behrndt, Holzmann, and Stelzer‐Landauer [Math. Nachr.
Jussi Behrndt, Markus Holzmann, Christian Stelzer‐Landauer   +2 more
wiley   +1 more source