American Institute of Mathematical Sciences

Advanced
June  2007, 6(2): 411-428. doi: 10.3934/cpaa.2007.6.411

Hardy type inequalities and Gaussian measure

Barbara Brandolini 1, , Francesco Chiacchio 1, and  Cristina Trombetti 1,

1. 

Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Universitario Monte S. Angelo, via Cintia, 80126 Napoli, Italy, Italy, Italy

Received  June 2006 Revised  January 2007 Published  March 2007

In this paper we prove some improved Hardy type inequalities with respect to the Gaussian measure. We show that they are strictly related to the well-known Gross Logarithmic Sobolev inequality. Some applications to elliptic P.D.E.'s are also given.
Keywords: degenerate elliptic P.D.E.'s., Gaussian symmetrization, Hardy type inequalities.
Mathematics Subject Classification: Primary: 46E30, 35J70; Secondary: 35J3.
Citation: Barbara Brandolini, Francesco Chiacchio, Cristina Trombetti. Hardy type inequalities and Gaussian measure. Communications on Pure & Applied Analysis, 2007, 6 (2) : 411-428. doi: 10.3934/cpaa.2007.6.411
[1]

Michal Fečkan, Vassilis Rothos. Bifurcations of periodics from homoclinics in singular O.D.E.: applications to discretizations of travelling waves of P.D.E.. Communications on Pure & Applied Analysis, 2002, 1 (4) : 475-483. doi: 10.3934/cpaa.2002.1.475
[2]

Michela Eleuteri. An existence result for a P.D.E. with hysteresis, convection and a nonlinear boundary condition. Conference Publications, 2007, 2007 (Special) : 344-353. doi: 10.3934/proc.2007.2007.344
[3]

Augusto Visintin. P.D.E.s with hysteresis 30 years later. Discrete & Continuous Dynamical Systems - S, 2015, 8 (4) : 793-816. doi: 10.3934/dcdss.2015.8.793
[4]

Juan Luis Vázquez, Nikolaos B. Zographopoulos. Hardy type inequalities and hidden energies. Discrete & Continuous Dynamical Systems, 2013, 33 (11&12) : 5457-5491. doi: 10.3934/dcds.2013.33.5457
[5]

Pradeep Boggarapu, Luz Roncal, Sundaram Thangavelu. On extension problem, trace Hardy and Hardy's inequalities for some fractional Laplacians. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2575-2605. doi: 10.3934/cpaa.2019116
[6]

Craig Cowan. Optimal Hardy inequalities for general elliptic operators with improvements. Communications on Pure & Applied Analysis, 2010, 9 (1) : 109-140. doi: 10.3934/cpaa.2010.9.109
[7]

Angelo Alvino, Roberta Volpicelli, Bruno Volzone. A remark on Hardy type inequalities with remainder terms. Discrete & Continuous Dynamical Systems - S, 2011, 4 (4) : 801-807. doi: 10.3934/dcdss.2011.4.801
[8]

C*-actions on C^3 are linearizable. S. Kaliman, M. Koras, L. Makar-Limanov and P. Russell. Electronic Research Announcements, 1997, 3: 63-71.

[9]

Panayotis Smyrnelis. Connecting orbits in Hilbert spaces and applications to P.D.E. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2797-2818. doi: 10.3934/cpaa.2020122
[10]

Jerome A. Goldstein, Ismail Kombe, Abdullah Yener. A unified approach to weighted Hardy type inequalities on Carnot groups. Discrete & Continuous Dynamical Systems, 2017, 37 (4) : 2009-2021. doi: 10.3934/dcds.2017085
[11]

Judith Vancostenoble. Improved Hardy-Poincaré inequalities and sharp Carleman estimates for degenerate/singular parabolic problems. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 761-790. doi: 10.3934/dcdss.2011.4.761
[12]

Filomena Feo, Pablo Raúl Stinga, Bruno Volzone. The fractional nonlocal Ornstein-Uhlenbeck equation, Gaussian symmetrization and regularity. Discrete & Continuous Dynamical Systems, 2018, 38 (7) : 3269-3298. doi: 10.3934/dcds.2018142
[13]

Elvise Berchio, Debdip Ganguly. Improved higher order poincaré inequalities on the hyperbolic space via Hardy-type remainder terms. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1871-1892. doi: 10.3934/cpaa.2016020
[14]

Jun Yang, Yaotian Shen. Weighted Sobolev-Hardy spaces and sign-changing solutions of degenerate elliptic equation. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2565-2575. doi: 10.3934/cpaa.2013.12.2565
[15]

Frank Merle, Hatem Zaag. O.D.E. type behavior of blow-up solutions of nonlinear heat equations. Discrete & Continuous Dynamical Systems, 2002, 8 (2) : 435-450. doi: 10.3934/dcds.2002.8.435
[16]

Lorenzo Brasco, Eleonora Cinti. On fractional Hardy inequalities in convex sets. Discrete & Continuous Dynamical Systems, 2018, 38 (8) : 4019-4040. doi: 10.3934/dcds.2018175
[17]

J.I. Díaz, D. Gómez-Castro. Steiner symmetrization for concave semilinear elliptic and parabolic equations and the obstacle problem. Conference Publications, 2015, 2015 (special) : 379-386. doi: 10.3934/proc.2015.0379
[18]

Gongbao Li, Tao Yang. Improved Sobolev inequalities involving weighted Morrey norms and the existence of nontrivial solutions to doubly critical elliptic systems involving fractional Laplacian and Hardy terms. Discrete & Continuous Dynamical Systems - S, 2021, 14 (6) : 1945-1966. doi: 10.3934/dcdss.2020469
[19]

Ismail Kombe, Abdullah Yener. A general approach to weighted $L^{p}$ Rellich type inequalities related to Greiner operator. Communications on Pure & Applied Analysis, 2019, 18 (2) : 869-886. doi: 10.3934/cpaa.2019042
[20]

Manli Song, Jinggang Tan. Hardy inequalities for the fractional powers of the Grushin operator. Communications on Pure & Applied Analysis, 2020, 19 (9) : 4699-4726. doi: 10.3934/cpaa.2020192

2020 Impact Factor: 1.916

Tools

Metrics

  • PDF downloads (294)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences