Free Access
Volume 21, Number 4, October-December 2015
Page(s) 924 - 938
Published online 20 May 2015
  1. V. Agostiniani and R. Magnanini, Symmetries in an overdetermined problem for the Green’s function. Discrete Contin. Dyn. Syst. Ser. S 4 (2011) 791–800. [CrossRef] [MathSciNet] [Google Scholar]
  2. A.D. Alexandrov, Uniqueness theorems for surfaces in the large I. Vestnik Leningrad Univ. Math. 11 (1956) 5–17. [Google Scholar]
  3. M. Birkner, J.A. López-Mimbela and A. Wakolbinger, Comparison results and steady states for the Fujita equation with fractional Laplacian. Ann. Inst. Henri Poincaré 22 (2005) 83–97. [CrossRef] [Google Scholar]
  4. I. Birindelli and F. Demengel, Overdetermined problems for some fully non linear operators. Comm. Partial Differ. Eq. 38 (2013) 608–628. [CrossRef] [Google Scholar]
  5. K. Bogdan and T. Byczkowski, Potential Theory of Schrödinger Operator based on fractional Laplacian. Probab. Math. Stat. 20 (2000) 293–335. [Google Scholar]
  6. B. Brandolini, C. Nitsch, P. Salani and C. Trombetti, Serrin-type overdetermined problems: an alternative proof. Arch. Ration. Mech. Anal. 190 (2008) 267–280. [CrossRef] [MathSciNet] [Google Scholar]
  7. F. Brock and A. Henrot, A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative. Rend. Circ. Mat. Palermo 51 (2002) 375–390. [CrossRef] [MathSciNet] [Google Scholar]
  8. G. Buttazzo, and B. Kawohl, Overdetermined boundary value problems for the ∞-laplacian. Int. Math. Res. Not. 2011 (2011) 237–247. [Google Scholar]
  9. W. Chen, C. Li and Biao Ou, Classification of solutions for an integral equation. Comm. Pure Appl. Math. 59 (2006) 330–343. [Google Scholar]
  10. M. Choulli and A. Henrot, Use of the domain derivative to prove symmetry results in partial differential equations. Math. Nachr. 192 (1998) 91–103. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Cianchi and P. Salani, Overdetermined anisotropic elliptic problems. Math. Ann. 345 (2009) 859–881. [CrossRef] [MathSciNet] [Google Scholar]
  12. F. Da Lio, and B. Sirakov, Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations. J. Eur. Math. Soc. (JEMS) 9 (2007) 317–330. [CrossRef] [MathSciNet] [Google Scholar]
  13. A.-L. Dalibard and D. Gérard-Varet, On shape optimization problems involving the fractional laplacian. ESAIM: COCV 19 (2013) 976–1013. [CrossRef] [EDP Sciences] [Google Scholar]
  14. E. di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s Guide to the Fractional Sobolev Spaces. Bull. Sci. Math. 136 (2012) 521–573. [CrossRef] [MathSciNet] [Google Scholar]
  15. B. Dyda, Fractional calculus for power functions and eigenvalues of the fractional Laplacian. Fract. Calc. Appl. Anal. 15 (2012) 536–555. [CrossRef] [MathSciNet] [Google Scholar]
  16. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton (1992). [Google Scholar]
  17. M.M. Fall, T. Weth, Monotonicity and nonexistence results for some fractional elliptic problems in the half space. Preprint (2013). Available online at: [Google Scholar]
  18. A. Farina and B. Kawohl, Remarks on an overdetermined boundary value problem. Calc. Var. Partial Differ. Eq. 31 (2008) 351–357. [CrossRef] [Google Scholar]
  19. A. Farina and E. Valdinoci, Flattening results for elliptic PDEs in unbounded domains with applications to overdetermined problems. Arch. Ration. Mech. Anal. 195 (2010) 1025–1058. [CrossRef] [MathSciNet] [Google Scholar]
  20. A. Farina and E. Valdinoci, Overdetermined problems in unbounded domains with Lipschitz singularities. Rev. Mat. Iberoam. 26 (2010) 965–974. [CrossRef] [MathSciNet] [Google Scholar]
  21. P. Felmer, A. Quaas and J. Tan, Positive solutions of Nonlinear Schrödinger equation with the fractional Laplacian. In Vol. 142A, Proc. of Roy. Soc. Edinburgh (2012). [Google Scholar]
  22. I. Fragalà and F. Gazzola, Partially overdetermined elliptic boundary value problems. J. Differ. Eq. 245 (2009) 1299–1322. [Google Scholar]
  23. I. Fragalà, F. Gazzola, and B. Kawohl, Overdetermined problems with possibly degenerate ellipticity, a geometric approach. Math. Z. 254 (2006) 117–132. [CrossRef] [MathSciNet] [Google Scholar]
  24. P. Felmer and Y. Wang, Radial symmetry of positive solutions involving the fractional Laplacian. Commun. Contemp. Math. (2013). Available at: [Google Scholar]
  25. N. Garofalo and J.L. Lewis, A symmetry result related to some overdetermined boundary value problems. Am. J. Math. 111 (1989) 9–33. [CrossRef] [Google Scholar]
  26. B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related problems via the maximum principle. Comm. Math. Phys. 68 (1979) 209–243. [Google Scholar]
  27. B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry of positive solutions of nonlinear equations. Math. Anal. Appl. Part A, Adv. Math. Suppl. Studies A 7 (1981) 369–402. [Google Scholar]
  28. L. Hauswirth, F. Hélein and F. Pacard, On an overdetermined elliptic problem. Pacific J. Math. 250 (2011) 319–334. [CrossRef] [MathSciNet] [Google Scholar]
  29. S. Jarohs, T. Weth, Asymptotic symmetry for a class of fractional reaction-diffusion equations. Discrete Contin. Dyn. Syst. 34 (2014) 2581–2615. [MathSciNet] [Google Scholar]
  30. G. Palatucci, O. Savin and E. Valdinoci, Local and global minimizers for a variational energy involving a fractional norm. Ann. Mat. Pura Appl. 192 (2013) 673–718. [Google Scholar]
  31. J. Prajapat, Serrin’s result for domains with a corner or cusp. Duke Math. J. 91 (1998) 29–31. [CrossRef] [MathSciNet] [Google Scholar]
  32. A.G. Ramm, Symmetry problem. Proc. Amer. Math. Soc. 141 (2013) 515–521. [CrossRef] [MathSciNet] [Google Scholar]
  33. W. Reichel, Radial symmetry for an electrostatic, a capillarity and some fully nonlinear overdetermined problems on exterior domains. Z. Anal. Anwendungen 15 (1996) 619–635. [CrossRef] [MathSciNet] [Google Scholar]
  34. W Reichel, Radial symmetry for elliptic boundary-value problems on exterior domains. Arch. Rational Mech. Anal. 137 (1997) 381–394. [CrossRef] [MathSciNet] [Google Scholar]
  35. X. Ros-Oton and J. Serra, The Dirichlet Problem for the fractional Laplacian: Regularity up to the boundary. J. Math. Pures Appl. 101 (2014) 275–302. [CrossRef] [MathSciNet] [Google Scholar]
  36. J. Serrin, A Symmetry Problem in Potential Theory. Arch. Rational Mech. Anal. 43 (1971) 304–318. [Google Scholar]
  37. L. Silvestre, Regularity of the obstacle problem for a fractional power of the Laplace operator. Comm. Pure Appl. Math. 60 (2007) 67–112. [CrossRef] [MathSciNet] [Google Scholar]
  38. L. Silvestre and B. Sirakov, Overdetermined problems for fully for fully nonlinear elliptic equations. Preprint (2013) available online at: [Google Scholar]
  39. B. Sirakov, Symmetry for exterior elliptic problems and two conjectures in potential theory. Ann. Inst. Henri Poincaré Anal. Non Lin. 18 (2001) 135–156. [CrossRef] [Google Scholar]
  40. H.F. Weinberger, Remark on the preceding paper of Serrin. Arch. Rational Mech. Anal. 43 (1971) 319–320. [CrossRef] [MathSciNet] [Google Scholar]
  41. T. Weth, Symmetry of solutions to variational problems for nonlinear elliptic equations via reflection methods. Jahresber. Deutsch. Math.-Ver. 112 (2010) 119–158. [CrossRef] [Google Scholar]
  42. S.Y. Yolcu, T. Yolcu, Estimates for the sums of eigenvalues of the fractional Laplacian on a bounded domain. Commun. Contemp. Math. 15 (2013) 1250048. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.