메뉴 건너뛰기




Volumn 304, Issue , 2017, Pages 300-354

Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case

Author keywords

Besov regularity; Fractional p Laplacian; Nonlocal elliptic equations

Indexed keywords


EID: 84986900072     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2016.03.039     Document Type: Article
Times cited : (129)

References (30)
  • 1
    • 0003362526 scopus 로고
    • Sobolev Spaces
    • Academic Press New York–London
    • [1] Adams, R.A., Sobolev Spaces. Pure and Applied Mathematics, vol. 65, 1975, Academic Press, New York–London.
    • (1975) Pure and Applied Mathematics , vol.65
    • Adams, R.A.1
  • 2
    • 70350120054 scopus 로고    scopus 로고
    • A nonlocal p-Laplacian evolution equation with nonhomogeneous Dirichlet boundary conditions
    • [2] Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J., A nonlocal p-Laplacian evolution equation with nonhomogeneous Dirichlet boundary conditions. SIAM J. Math. Anal. 40 (2009), 1815–1851.
    • (2009) SIAM J. Math. Anal. , vol.40 , pp. 1815-1851
    • Andreu, F.1    Mazón, J.M.2    Rossi, J.D.3    Toledo, J.4
  • 3
    • 84861004575 scopus 로고    scopus 로고
    • Non-local gradient dependent operators
    • [3] Bjorland, C., Caffarelli, L., Figalli, A., Non-local gradient dependent operators. Adv. Math. 230 (2012), 1859–1894.
    • (2012) Adv. Math. , vol.230 , pp. 1859-1894
    • Bjorland, C.1    Caffarelli, L.2    Figalli, A.3
  • 7
    • 84989869669 scopus 로고    scopus 로고
    • The second eigenvalue of the fractional p-Laplacian
    • in press
    • [7] Brasco, L., Parini, E., The second eigenvalue of the fractional p-Laplacian. Adv. Calc. Var., 2016, 10.1515/acv-2015-0007 in press.
    • (2016) Adv. Calc. Var.
    • Brasco, L.1    Parini, E.2
  • 8
    • 84943525413 scopus 로고    scopus 로고
    • Stability of variational eigenvalues for the fractional p-Laplacian
    • [8] Brasco, L., Parini, E., Squassina, M., Stability of variational eigenvalues for the fractional p-Laplacian. Discrete Contin. Dyn. Syst. 36 (2016), 1813–1845.
    • (2016) Discrete Contin. Dyn. Syst. , vol.36 , pp. 1813-1845
    • Brasco, L.1    Parini, E.2    Squassina, M.3
  • 9
    • 84986917238 scopus 로고    scopus 로고
    • On nonlocal quasilinear equations and their local limits
    • preprint, available at
    • [9] Chasseigne, E., Jakobsen, E., On nonlocal quasilinear equations and their local limits. preprint, available at http://arxiv.org/abs/1503.06939, 2015.
    • (2015)
    • Chasseigne, E.1    Jakobsen, E.2
  • 10
    • 84986908957 scopus 로고    scopus 로고
    • Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces
    • preprint, available at
    • [10] Cozzi, M., Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces. preprint, available at http://arxiv.org/abs/1601.02819, 2015.
    • (2015)
    • Cozzi, M.1
  • 13
    • 84964692143 scopus 로고    scopus 로고
    • Existence results for fractional p-Laplacian problems via Morse theory
    • [13] Iannizzotto, A., Liu, S., Perera, K., Squassina, M., Existence results for fractional p-Laplacian problems via Morse theory. Adv. Calc. Var. 9 (2016), 101–125.
    • (2016) Adv. Calc. Var. , vol.9 , pp. 101-125
    • Iannizzotto, A.1    Liu, S.2    Perera, K.3    Squassina, M.4
  • 15
    • 85006953017 scopus 로고    scopus 로고
    • Global Hölder regularity for the fractional p-Laplacian
    • available at in press
    • [15] Iannizzotto, A., Mosconi, S., Squassina, M., Global Hölder regularity for the fractional p-Laplacian. Rev. Mat. Iberoam., 2016 available at http://arxiv.org/abs/1411.2956 in press.
    • (2016) Rev. Mat. Iberoam.
    • Iannizzotto, A.1    Mosconi, S.2    Squassina, M.3
  • 16
    • 77949774164 scopus 로고    scopus 로고
    • A class of integral equations and approximation of p-Laplace equations
    • [16] Ishii, H., Nakamura, G., A class of integral equations and approximation of p-Laplace equations. Calc. Var. Partial Differential Equations 37 (2010), 485–522.
    • (2010) Calc. Var. Partial Differential Equations , vol.37 , pp. 485-522
    • Ishii, H.1    Nakamura, G.2
  • 17
    • 54849198100 scopus 로고    scopus 로고
    • A priori estimates for integro-differential operators with measurable kernels
    • [17] Kassmann, M., A priori estimates for integro-differential operators with measurable kernels. Calc. Var. Partial Differential Equations 34 (2009), 1–21.
    • (2009) Calc. Var. Partial Differential Equations , vol.34 , pp. 1-21
    • Kassmann, M.1
  • 19
    • 84929758705 scopus 로고    scopus 로고
    • Nonlocal self-improving properties
    • [19] Kuusi, T., Mingione, G., Sire, Y., Nonlocal self-improving properties. Anal. PDE 8 (2015), 57–114.
    • (2015) Anal. PDE , vol.8 , pp. 57-114
    • Kuusi, T.1    Mingione, G.2    Sire, Y.3
  • 20
    • 84928738414 scopus 로고    scopus 로고
    • Nonlocal equations with measure data
    • [20] Kuusi, T., Mingione, G., Sire, Y., Nonlocal equations with measure data. Comm. Math. Phys. 337 (2015), 1317–1368.
    • (2015) Comm. Math. Phys. , vol.337 , pp. 1317-1368
    • Kuusi, T.1    Mingione, G.2    Sire, Y.3
  • 21
    • 84986881545 scopus 로고    scopus 로고
    • Hölder estimates for viscosity solutions of equations of fractional p-Laplace type
    • preprint, available at
    • [21] Lindgren, E., Hölder estimates for viscosity solutions of equations of fractional p-Laplace type. preprint, available at http://arxiv.org/abs/1405.6612, 2014.
    • (2014)
    • Lindgren, E.1
  • 23
    • 0038610614 scopus 로고    scopus 로고
    • The singular set of solutions of non-differentiable elliptic systems
    • [23] Mingione, G., The singular set of solutions of non-differentiable elliptic systems. Arch. Ration. Mech. Anal. 166 (2003), 287–301.
    • (2003) Arch. Ration. Mech. Anal. , vol.166 , pp. 287-301
    • Mingione, G.1
  • 24
    • 35448932506 scopus 로고    scopus 로고
    • The Calderón-Zygmund theory for elliptic problems with measure data
    • [24] Mingione, G., The Calderón-Zygmund theory for elliptic problems with measure data. Ann. Sc. Norm. Super. Pisa Cl. Sci. 6 (2007), 195–261.
    • (2007) Ann. Sc. Norm. Super. Pisa Cl. Sci. , vol.6 , pp. 195-261
    • Mingione, G.1
  • 25
    • 1142288658 scopus 로고    scopus 로고
    • A new approach to Sobolev spaces and connections to Γ-convergence
    • [25] Ponce, A., A new approach to Sobolev spaces and connections to Γ-convergence. Calc. Var. Partial Differential Equations 19 (2004), 229–255.
    • (2004) Calc. Var. Partial Differential Equations , vol.19 , pp. 229-255
    • Ponce, A.1
  • 26
    • 84951772067 scopus 로고    scopus 로고
    • Nonlinear commutators for the fractional p-Laplacian and applications
    • [26] Schikorra, A., Nonlinear commutators for the fractional p-Laplacian and applications. Math. Ann., 2016 available at http://dx.doi.org/10.1007/s00208-015-1347-0 in press.
    • (2016) Math. Ann.
    • Schikorra, A.1
  • 27
    • 70449581236 scopus 로고    scopus 로고
    • Rigidity results for some boundary quasilinear phase transitions
    • [27] Sire, Y., Valdinoci, E., Rigidity results for some boundary quasilinear phase transitions. Comm. Partial Differential Equations 34 (2009), 765–784.
    • (2009) Comm. Partial Differential Equations , vol.34 , pp. 765-784
    • Sire, Y.1    Valdinoci, E.2
  • 28
    • 0003201639 scopus 로고
    • Singular Integrals and Differentiability Properties of Functions
    • Princeton University Press Princeton, N.J.
    • [28] Stein, E., Singular Integrals and Differentiability Properties of Functions. Princeton Math. Ser., vol. 30, 1970, Princeton University Press, Princeton, N.J.
    • (1970) Princeton Math. Ser. , vol.30
    • Stein, E.1
  • 29
    • 0003216183 scopus 로고
    • Theory of Function Spaces. II
    • Birkhäuser Verlag Basel
    • [29] Triebel, H., Theory of Function Spaces. II. Monogr. Math., vol. 84, 1992, Birkhäuser Verlag, Basel.
    • (1992) Monogr. Math. , vol.84
    • Triebel, H.1
  • 30
    • 0000968617 scopus 로고
    • Regularity for a class of non-linear elliptic systems
    • [30] Uhlenbeck, K., Regularity for a class of non-linear elliptic systems. Acta Math. 138 (1977), 219–240.
    • (1977) Acta Math. , vol.138 , pp. 219-240
    • Uhlenbeck, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.