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Oblique derivative problems for elliptic and parabolic equations
A Brezis-Nirenberg result for non-local critical equations in low dimension
1. | Dipartimento di Matematica, Università degli Studi della Calabria, Ponte Pietro Bucci 31B, I–87036 Arcavacata di Rende |
2. | Università di Roma Tor Vergata, Dipartimento di Matematica, Via della Ricerca Scientifica, I-00133 Rome |
References:
[1] |
J. Funct. Anal., 14 (1973), 349-381.
doi: 10.1016/0022-1236(73)90051-7. |
[2] |
J. Differential Equations, 252 (2012), 6133-6162.
doi: 10.1016/j.jde.2012.02.023. |
[3] |
Proc. Amer. Math. Soc., 88 (1983), 486-490.
doi: 10.1090/S0002-9939-1983-0699419-3. |
[4] |
Comm. Pure Appl. Math., 36 (1983), 437-477.
doi: 10.1002/cpa.3160360405. |
[5] |
Ann. Inst. H. Poincaré Anal. Non Linéaire, 2 (1985), 463-470. |
[6] |
Nonlinear Anal., 17 (1991), 445-455.
doi: 10.1016/0362-546X(91)90139-R. |
[7] |
J. Math. Anal. Appl., 295 (2004), 225-236.
doi: 10.1016/j.jmaa.2004.03.034. |
[8] |
Bull. Sci. Math., 136 (2012), 521-573.
doi: 10.1016/j.bulsci.2011.12.004. |
[9] |
Ann. Inst. H. Poincaré Anal. Non Linéaire, 19 (2002), 125-142. |
[10] |
A. Fiscella, Saddle point solutions for non-local elliptic operators,, preprint., (). Google Scholar |
[11] |
Adv. Differential Equations, 2 (1997), 555-572. |
[12] |
Ann. Scuola Norm. Sup. Pisa Cl. Sci., 5 (1978), 215-223. |
[13] |
CBMS Reg. Conf. Ser. Math., 65, American Mathematical Society, Providence, RI, 1986. |
[14] |
R. Servadei, The Yamabe equation in a non-local setting,, preprint, (): 12. Google Scholar |
[15] |
to appear in Rev. Mat. Iberoam., 29 (2013). Google Scholar |
[16] |
J. Math. Anal. Appl., 389 (2012), 887-898.
doi: 10.1016/j.jmaa.2011.12.032. |
[17] |
Discrete Contin. Dyn. Syst., 33 (2013), 2105-2137.
doi: 10.3934/dcds.2013.33.2105. |
[18] |
R. Servadei and E. Valdinoci, The Brezis-Nirenberg result for the fractional Laplacian,, to appear in Trans. Amer. Math. Soc., (). Google Scholar |
[19] |
R. Servadei and E. Valdinoci, Fractional Laplacian equations with critical Sobolev exponent,, preprint, (): 12. Google Scholar |
[20] |
Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, Springer Verlag, Berlin-Heidelberg, 1990. |
[21] |
Calc. Var. Partial Differential Equations, 36 (2011), 21-41. |
[22] |
Progress in Nonlinear Differential Equations and their Applications, 24, Birkhäuser, Boston, 1996. |
show all references
References:
[1] |
J. Funct. Anal., 14 (1973), 349-381.
doi: 10.1016/0022-1236(73)90051-7. |
[2] |
J. Differential Equations, 252 (2012), 6133-6162.
doi: 10.1016/j.jde.2012.02.023. |
[3] |
Proc. Amer. Math. Soc., 88 (1983), 486-490.
doi: 10.1090/S0002-9939-1983-0699419-3. |
[4] |
Comm. Pure Appl. Math., 36 (1983), 437-477.
doi: 10.1002/cpa.3160360405. |
[5] |
Ann. Inst. H. Poincaré Anal. Non Linéaire, 2 (1985), 463-470. |
[6] |
Nonlinear Anal., 17 (1991), 445-455.
doi: 10.1016/0362-546X(91)90139-R. |
[7] |
J. Math. Anal. Appl., 295 (2004), 225-236.
doi: 10.1016/j.jmaa.2004.03.034. |
[8] |
Bull. Sci. Math., 136 (2012), 521-573.
doi: 10.1016/j.bulsci.2011.12.004. |
[9] |
Ann. Inst. H. Poincaré Anal. Non Linéaire, 19 (2002), 125-142. |
[10] |
A. Fiscella, Saddle point solutions for non-local elliptic operators,, preprint., (). Google Scholar |
[11] |
Adv. Differential Equations, 2 (1997), 555-572. |
[12] |
Ann. Scuola Norm. Sup. Pisa Cl. Sci., 5 (1978), 215-223. |
[13] |
CBMS Reg. Conf. Ser. Math., 65, American Mathematical Society, Providence, RI, 1986. |
[14] |
R. Servadei, The Yamabe equation in a non-local setting,, preprint, (): 12. Google Scholar |
[15] |
to appear in Rev. Mat. Iberoam., 29 (2013). Google Scholar |
[16] |
J. Math. Anal. Appl., 389 (2012), 887-898.
doi: 10.1016/j.jmaa.2011.12.032. |
[17] |
Discrete Contin. Dyn. Syst., 33 (2013), 2105-2137.
doi: 10.3934/dcds.2013.33.2105. |
[18] |
R. Servadei and E. Valdinoci, The Brezis-Nirenberg result for the fractional Laplacian,, to appear in Trans. Amer. Math. Soc., (). Google Scholar |
[19] |
R. Servadei and E. Valdinoci, Fractional Laplacian equations with critical Sobolev exponent,, preprint, (): 12. Google Scholar |
[20] |
Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, Springer Verlag, Berlin-Heidelberg, 1990. |
[21] |
Calc. Var. Partial Differential Equations, 36 (2011), 21-41. |
[22] |
Progress in Nonlinear Differential Equations and their Applications, 24, Birkhäuser, Boston, 1996. |
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