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A weighted anisotropic Sobolev type inequality and its applications to Hardy inequalities

  • Giuseppina di Blasio
  • Giovanni PisanteEmail author
  • Georgios Psaradakis
Article
  • 62 Downloads

Abstract

In this paper we focus our attention on an embedding result for a weighted Sobolev space that involves as weight the distance function from the boundary taken with respect to a general smooth gauge function F. Starting from this type of inequalities we prove some refined Hardy-type inequalities.

Mathematics Subject Classification

53C60 58J60 26D10 46E35 

Notes

Acknowledgements

G. di Blasio and G. Pisante are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the IstitutoNazionale di Alta Matematica (INdAM) whose support through the GNAMPA Project 2019 Pogram (U-UFMBAZ-2019-000477 11-03-2019) is gratefully acknowledged. G Pisante and G. Psaradakis also acknowledge the INdAM-GNAMPA for the Visiting Professor Program 2018 (U-FMBAZ-2018-001525 18-12-2018). G. Psaradakis was supported in part from Università degli Studi della Campania “Luigi Vanvitelli” (D.R. 0950-2017) through a visiting researcher position. The authors are grateful to both referees whose remarks and suggestions helped us to considerably enhance the initial version of the article.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Dipartimento di Matematica e FisicaUniversità degli Studi della Campania “L. Vanvitelli”CasertaItaly
  2. 2.Lehrstuhl für Mathematik IVWIM-Universität Mannheim B6 28MannheimGermany

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