158
Views
17
CrossRef citations to date
0
Altmetric
Original Articles

Brunn-Minkowski inequalities for two functionals involving the p-Laplace operator

, &
Pages 45-66 | Received 14 Oct 2003, Accepted 27 Apr 2004, Published online: 25 Jan 2007

References

  • Colesanti , A and Salani , P . 2003 . The Brunn-Minkowski inequality for p-capacity of convex bodies . Mathematische Annalen , 327 ( 3 ) : 459 – 479 .
  • Colesanti , A and Cuoghi , P . 2003 . The Brunn-Minkowski inequality for the n-dimensional logarithmic capacity . preprint
  • Salani , P . 2005 . A Brunn-Minkowski inequality for the Monge-Ampère eigenvalue . Advances in Mathematics , 194 ( 1 ) : 67 – 86 .
  • Colesanti , A . 2005 . Brunn-Minkowski inequalities for variational functionals and related problems . Advances in Mathematics , 194 ( 1 ) : 105 – 140 .
  • Schneider , R . 1993 . Convex Bodies: the Brunn-Minkowski Theory , Cambridge University Press : Cambridge .
  • Gardner , RJ . 2002 . The Brunn-Minkowski inequality . Bulletin American Mathematical Society (N.S.) , 39 ( 3 ) : 355 – 405 .
  • Brascamp , HJ and Lieb , EH . 1976 . On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log-concave functions, and with an application to the diffusion equation . Journal of Functional Analysis , 22 : 366 – 389 .
  • Borell , C . 1984 . Capacitary inequalities of Brunn-Minkowski type . Mathematische Annalen , 263 : 179 – 184 .
  • Borell , C . 1984 . Hitting probability of killed Brownian motion: a study on geometric regularity . Annales Scientifiques de l'Ecole Normale Superieure Paris , 17 : 451 – 467 .
  • Borell , C . 1985 . Greenian potentials and concavity . Mathematische Annalen , 272 : 155 – 160 .
  • Caffarelli , LA , Jerison , D and Lieb , EH . 1996 . On the case of equality in the Brunn-Minkowski inequality for capacity . Advances in Mathematics , 117 n.2 : 193 – 207 .
  • Sakaguchi , S . 1987 . Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems . Annali della Scuola Normale Superiore di Pisa, IV serie , 14 : 403 – 421 .
  • Pólya , G and Szegö , G . 1951 . Isoperimetric Inequalities in Mathematical Physics , Princeton : Princeton University Press .
  • Korevaar , NJ . 1983 . Capillary surface convexity above convex domains . Indiana University Mathematics Journal , 32 : 73 – 81 .
  • Kennington , AU . 1985 . Power concavity and boundary value problems . Indiana University Mathematics Journal , 34 ( 3 ) : 687 – 704 .
  • Rockafellar , RT . 1970 . Convex Analysis , Princeton, New Jersey : Princeton University Press .
  • Alvarez , G , Lasry , J-M and Lions , P-L . 1997 . Convex viscosity solutions and state constraints . Journal de Mathematiques Pures et Appliquees , 76 : 265 – 288 .
  • Korevaar , NJ and Lewis , JL . 1987 . Convex solutions of certain elliptic equations have constant rank Hessians . Archive for Rational Mechanics and Analysis , 97 ( 1 ) : 19 – 32 .
  • Tolksdorf , P . 1983 . On the Dirichlet problem for quasilinear equations in domains with conical boundary points . Comm. P.D.E. , 8 : 773 – 817 .
  • Tolksdorf , P . 1984 . Regularity for a more general class of quasilinear elliptic equations . Journal of Differential Equations , 51 : 126 – 150 .
  • Dubuc , S . 1977 . Critères di convexité et inégalités intégrales . Annales de l'Institut Fourier, Grenoble 27 , 1 : 135 – 165 .
  • Belloni , M and Kawohl , B . 2002 . A direct uniqueness proof for equations involving the p-Laplace operato . Manuscripta Mathematica , 109 : 229 – 231 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.