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All issues Volume 21 / No 4 (October-December 2015) ESAIM: COCV, 21 4 (2015) 924-938 References
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Issue
ESAIM: COCV
Volume 21, Number 4, October-December 2015
Page(s) 924 - 938
DOI https://doi.org/10.1051/cocv/2014048
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: http://arxiv.org/abs/1309.7230. [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: http://www.worldscientific.com/doi/pdf/10.1142/S0219199713500235. [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: http://arxiv.org/abs/1306.6673. [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]

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