An eigenvalue problem related to Hardy’s L P inequality
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 29 (2000) no. 3, p. 581-604
@article{ASNSP_2000_4_29_3_581_0,
     author = {Marcus, Moshe and Shafrir, Itai},
     title = {An eigenvalue problem related to Hardy's $L^P$ inequality},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {3},
     year = {2000},
     pages = {581-604},
     zbl = {1008.49034},
     mrnumber = {1817710},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2000_4_29_3_581_0}
}
Marcus, Moshe; Shafrir, Itai. An eigenvalue problem related to Hardy’s $L^P$ inequality. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 29 (2000) no. 3, pp. 581-604. http://www.numdam.org/item/ASNSP_2000_4_29_3_581_0/

[1] A. Anane, Simplicité et isolation de la première valeur propre du p-laplacien avec poids, C. R. Acad. Sci. Paris Sèr. I-Math. 305 (1987), 725-728. | MR 920052 | Zbl 0633.35061

[2] A. Ancona, Une propriété des espaces de Sobolev, C. R. Acad. Sci. Paris Sér. I 292 (1981), 477-480. | MR 612540 | Zbl 0461.46028

[3] A. Ancona, On strong barriers and inequality of Hardy for domains in Rn, J. London Math. Soc. 34 (1986), 274-290. | MR 856511 | Zbl 0629.31002

[4] W. Allegretto - Y.X. Huang, A Picone's identity for the p-Laplacian and applications, Nonlinear Anal. 32 (1998), 819-830. | MR 1618334 | Zbl 0930.35053

[5] H. Brezis - M. Marcus, Hardy's inequality revisited, Ann. Scuola Norm. Sup. Pisa. Cl. Sci. 25 (1997), 217-237. | Numdam | MR 1655516 | Zbl 1011.46027

[6] H. Brezis - M. Marcus - I. Shafrir, Extremal functions for Hardy's inequality with weight, J. Funct. Anal. 171 (2000), 177-191. | MR 1742864 | Zbl 0953.26006

[7] H. Brezis - L. Oswald, Remarks on sublinear elliptic equations, Nonlinear Anal. 10 (1986), 55-64. | MR 820658 | Zbl 0593.35045

[8] E.B. Davies, The Hardy constant, Quart. J. Math. Oxford 46 (1995), 417-431. | MR 1366614 | Zbl 0857.26005

[9] E. Di Benedetto, C1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983). | Zbl 0539.35027

[10] J.I. Diaz - J.E. Saa, Existence et unicité de solutions positives pour certains équations elliptiques quasilinéaires de la première, C. R. Acad. Sci. Paris Sér. I 305 (1987), 521-524. | MR 916325 | Zbl 0656.35039

[11] D. Gilbarg - N. Trudinger, "Elliptic Partial Differential Equations of Elliptic Type", 2nd ed., Springer-Verlag, Berlin-Heidelberg, 1983. | MR 737190

[12] P. Hajlasz, Pointwise Hardy inequalities, Proc. Amer. Math. Soc. 127 (1999), 417-423. | MR 1458875 | Zbl 0911.31005

[13] G.H. Hardy, Note on a Theorem of Hilbert, Math. 6 (1920), 314-317. | JFM 47.0207.01 | MR 1544414

[14] G.H. Hardy, An inequality between integrals, Messenger of Math. 54 (1925), 150-156. | JFM 51.0192.01

[15] A. Kufner, "Weighted Sobolev Spaces", John Wiley & Sons, 1985. | MR 802206 | Zbl 0567.46009

[16] P. Lindquist, On the equation div (|∇u| p-2∇u) + λ|u|p-2|u = 0, Proc. Amer. Math. Soc. 109 (1990), 157-164. | Zbl 0714.35029

[17] J.L. Lewis, Uniformly fat sets, Trans. Amer. Math. Soc. 308 (1988), 177-196. | MR 946438 | Zbl 0668.31002

[18] M. Marcus - V.J. Mizel - Y. Pinchover, On the best constant for Hardy's inequality in Rn, Trans. Amer. Math. Soc. 350 (1998), 3237-3255. | MR 1458330 | Zbl 0917.26016

[19] T. Matskewich - P.E. Sobolevskii, The best possible constant in a generalized Hardy's inequality for convex domains in Rn, Nonlinear Anal. 28 (1997), 1601-1610. | MR 1431208 | Zbl 0876.46025

[20] J Nečas, Sur une méthode pour résoudre les équations aux dérivées partielles du type elliptique, voisine de la variationelle, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 16 (1962), 305-326. | Numdam | MR 163054 | Zbl 0112.33101

[21] B. Opic - A. Kufner, "Hardy-type Inequalities", Pitman Research Notes in Math., Vol. 219, Longman, 1990. | MR 1069756 | Zbl 0698.26007

[22] J. Serrin, Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964), 247-302. | MR 170096 | Zbl 0128.09101

[23] I. Shafrir, On the asymptotic behavior of minimizing sequences for Hardy's inequality, Comm. Contemp. Math. 2 (2000), 1-38. | MR 1759788 | Zbl 0956.35036

[24] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984), 121-150. | MR 727034 | Zbl 0488.35017

[25] N. Trudinger, On Harnack type inequalities and their applications quasilinear elliptic equations, Comm. Pure Appl. Math. 20 (1967), 721-747. | MR 226198 | Zbl 0153.42703

[26] A. Wannebo, Hardy inequalities, Proc. A.M.S. 109 (1990), 85-95. | MR 1010807 | Zbl 0715.26009