Publication Cover
Applicable Analysis
An International Journal
Volume 84, 2005 - Issue 12
123
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

Starshapedness of level sets of solutions to elliptic PDEs

Pages 1185-1197 | Received 01 Jan 2002, Accepted 02 Apr 2004, Published online: 04 Sep 2006

References

  • Acker , A . 1994 . On the uniqueness, monotonicity, starlikeness and convexity of solutions for a nonlinear boundary value problem in elliptic PDEs . Nonlinear Analysis. Theory, Methods & Applications , 22 ( 6 ) : 697 – 705 .
  • Caffarelli , L , Nirenberg , L and Spruck , J . 1985 . The Dirichlet problem for nonlinear elliptic equations, III: functions of the eigenvalues of the Hessian . Acta Mathematica , 155 : 261 – 301 .
  • Colesanti , A , Francini , E and Salani , P . 2000 . Convexity and asymptotic estimates for large solutions of Hessian equations . Differential Integral Equations 13 , 10–12 : 1459 – 1472 .
  • Colesanti , A and Salani , P . 2003 . Quasi-convex envelope of a function and convexity of level sets of solutions to elliptic equations . Mathematische Nachrichten , 258 : 3 – 15 .
  • Crandall , MG , Ishii , H and Lions , PL . 1992 . User's guide to viscosity solutions of second order elliptic PDE . American Mathematical Society. Bulletin , 27 ( 1 ) : 1 – 67 .
  • Diaz , JI and Kawohl , B . 1993 . On convexity and starshapedness of level sets for some nonlinear elliptic and parabolic problems on convex rings . Journal of Mathematical Analysis and Applications , 177 ( 1 ) : 263 – 286 .
  • Francini , E . 1996 . Starshapedness of level sets for solutions of nonlinear parabolic equations . Rendiconti dell'Istituto di Matematica dell'Universita di Trieste , 28 ( 1–2 ) : 49 – 62 .
  • Francini , E . 1998 . Starshapedness of level sets for solutions of nonlinear elliptic equations . Mathematische Nachrichten , 193 : 49 – 56 .
  • Francini , E and Greco , A . 1998 . Blow-up in exterior domains: existence and starshapedness . Zeitschrift fur Analysis und ihre Anwendungen , 17 ( 2 ) : 431 – 441 .
  • Greco , A and Reichel , W . 2001 . Existence and starshapedness for the Lane-Emden equation . Applicable Analysis , 78 ( 1–2 ) : 21 – 23 .
  • Jensen , R . 1998 . Viscosity solutions of elliptic partial differential equations . Doc. Math. J. DMV , ICM ( III ) : 31 – 38 .
  • Kawohl B 1985 Rearrangements and convexity of level sets in P.D.E. Lecture Notes in Mathematics, 1150 Berlin Springer
  • Kawohl B 1986 Geometrical properties of level sets of solutions to elliptic ring problems Symposium in Pure Mathematics 45, Part II 541 556
  • Kawohla , B and Kutev , N . 1998 . Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations . Archives of Mathematics , 70 : 470 – 478 .
  • Longinetti , M . 1985 . A maximum principle for the starshape of solutions of nonlinear Poisson equations . Boll. , UMI 6 ( 4-A ) : 91 – 96 .
  • Trudinger , N . 1997 . Weak solutions of Hessian equations . Communications in Partial Differential Equations , 22 : 1251 – 1261 .

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.