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Articles

On vs. local minimizers for a critical functional related to fractional p-Laplacian

Pages 1586-1595 | Received 11 Oct 2016, Accepted 13 Mar 2017, Published online: 31 Mar 2017

References

  • Iannizzotto A, Mosconi S, Squassina M. Hs vs. C0-weighted minimizers. NoDEA Nonlinear Differ Equ Appl. 2015;22(3):477–497.
  • Ros-Oton X, Serra J. The Dirichlet problem for the fractional Laplacian: regularity up to the boundary. J Math Pures Appl. 2014;101:275–302.
  • Ros-Oton X, Serra J. Boundary regularity for fully nonlinear integro-differential equations. Duke Math J. 2016;165(11):2079–2154.
  • Brezis H, Nirenberg L. Minima locaux relatifs à C1 et H1. CR Acad Sci Paris sér I Math. 1993;317:465–472.
  • Ambrosetti A, Brezis H, Cerami G. Combined effects of concave and convex nonlinearities in some elliptic problems. J Funct Anal. 1994;122:519–543.
  • Iannizzotto A, Liu S, Perera K, Squassina M. Existence results for fractional p-Laplacian problems via Morse theory. Adv Calc Var. 2016;9(2):101–125.
  • Ambrosetti A, Rabinowitz PH. Dual variational methods in critical point theory and applications. J Funct Anal. 1973;14:349–381.
  • García Azorero JP, Peral Alonso I, Manfredi JJ. Sobolev vs. Hölder local minimizers and global multiplicity for some quasilinear elliptic equations. Commun Contemp Math. 2000;2(3):385–404.
  • Lieberman G. Boundary regularity for solutions of degenerate elliptic equations. Nonlinear Anal. 1988;12(11):1203–1219.
  • DiBenedetto E. C1+α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. 1983;7(8):827–850.
  • Brock F, Iturraga L, Ubilla P. A multiplicity result for the p-Laplacien involving a parameter. Ann Henri Poincaré. 2008;9(7):1371–1386.
  • DeFigueiredo DG, Gossez JP, Ubilla P. Local “superlinearity” and “sublinearity” for the p-Laplacian. J Funct Anal. 2009;257:721–752.
  • Giacomoni J, Saoudi K. W1,p0 vs. C1 local minimizers for a singular and critical functional. J Math Anal Appl. 2010;363(2):697–710.
  • Saoudi K. W1,p(x)0 vs. C1 local minimizers for a functional with critical growth. J Partial Differ Equ. 2014;27(2):115–124.
  • Saoudi K. W1,N vs. C1 local minimizer for a singular functional with Neumann boundary condition. accepted for publication in Boletim da Sociedade Paranaense de Matem\’{a}tica.
  • Saoudi K. Existence and multiplicity of solutions for a quasilinear equation involving the p(x)--Laplace operator. Complex Var Elliptic Equ. 2017;62(3):318–332.
  • Saoudi K, Ghanmi A. A multiplicity results for a singular equation involving the p(x)--Laplace operator. Complex Var Elliptic Equ. 2017;62(5):695–725.
  • Saoudi K, Kratou M. Existence of multiple solutions for a singular and quasilinear equation. Complex Var Elliptic Equ. 2015;60(7):893–925.
  • Saoudi K, Kratou M, Al Sadhan S. Multiplicity results for the p(x)--Laplacian equation with singular nonlinearities and nonlinear Neumann boundary condition. Int J Differ Equ. 2016, Art. ID 3149482, 14 pp.
  • Brasco L, Lindgren E, Parini E. The fractional Cheeger problem. Interfaces and Free Boundaries. 2014;16(2):419–458.
  • Franzina G, Palatucci G. Fractional p-eigenvalues. Riv Mat Univ Parma. 2014;5(2):373–386.
  • Iannizzotto A, Mosconi S, Squassina M. Global Hölder regularity for the fractional pLaplacian. Rev Mat Iberoam. 2016;32(4):1353–1392.

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