Some hardy type inequalities with finsler norms

References

[1] Alvino, A—Ferone, A.—Mercaldo, A.—Takahashi, F.—Volpicelli, R.: Finsler Hardy-Kato’s inequality, J. Math. Anal. Appl. 470(1) (2019), 360–374.10.1016/j.jmaa.2018.10.008Suche in Google Scholar

[2] Arendt, W.—Goldstein, G. R.—Goldstein, J. A.: Outgrowths of Hardy’s inequality. In: Recent Advances in Differential Equations and Mathematical Physics (N. Chernov, Y. Karpeshina, I. W. Knowles, R. T. Lewis, and R. Weikard (eds.)), Contemp. Math. 412, 51–68, 2006.10.1090/conm/412/07766Suche in Google Scholar

[3] Balinsky, A. A.—Evans, W. D.—Lewis, R. T.: The Analysis and Geometry of Hardy’s Inequality, Universitext, Springer, Cham, 2015.10.1007/978-3-319-22870-9Suche in Google Scholar

[4] Bogdan, K.—Dyda, B.—Kim, P.: Hardy inequalities and non-explosion results for semigroups, Potential Anal. 44 (2016), 229–247.10.1007/s11118-015-9507-0Suche in Google Scholar

[5] Çağı, A.: Finsler Geometry and its Applications to Electromagnetism, PhD diss., METU, 2003.Suche in Google Scholar

[6] Cianchi, A.—Ferone, A.: Hardy inequalities with non-standard remainder terms, Ann. Inst. H. Poincaré. Anal. Non Linéaire 25 (2008), 889–906.10.1016/j.anihpc.2007.05.003Suche in Google Scholar

[7] Clayton, J. D.: On Finsler geometry and applications in mechanics: review and new perspectives. Adv. Math. Phys. (2015), Art. ID 828475.10.1155/2015/828475Suche in Google Scholar

[8] Davies, E. B.: Heat Kernels and Spectral Theory. Cambridge Tracts in Math., Vol. 92, Cambridge Univ. Press, Cambridge, 1989.10.1017/CBO9780511566158Suche in Google Scholar

[9] Davies, E. B.: Spectral Theory and Differential Operators, Cambridge University Press, Cambridge, 1995.10.1017/CBO9780511623721Suche in Google Scholar

[10] Della Pietra, F.—di Blasio, G.—Gavitone, N.: Anisotropic Hardy inequalities, Proc. Roy. Soc. Edinburgh Sect. A 148(3) (2018), 483–498.10.1017/S0308210517000336Suche in Google Scholar

[11] Dolbeault, J.—Volzone, B.: Improved Poincaré inequalities, Nonlinear Anal. 75 (2012), 5985–6001.10.1016/j.na.2012.05.008Suche in Google Scholar

[12] Duy, N. T.—Lam, N.—Triet, N. A.: Hardy and Rellich inequalities with exact missing terms on homogeneous groups, J. Math. Soc. Japan 71(4) (2019), 1243–1256.10.2969/jmsj/80878087Suche in Google Scholar

[13] Duy, N. T.—Lam, N.—Triet, N. A.: Hardy-Rellich identities with Bessel pairs, Arch. Math. (Basel) 113(1) (2019), 95–112.10.1007/s00013-019-01305-wSuche in Google Scholar

[14] Duy, N. T.—Lam, N.—Triet, N. A.: Improved Hardy and Hardy-Rellich type inequalities with Bessel pairs via factorizations, J. Spectr. Theory 10(4) (2020), 1277–1302.10.4171/JST/327Suche in Google Scholar

[15] Duy, N. T.—Lam, N.—Triet, N. A.—Yin, W.: Improved Hardy inequalities with exact remainder terms, Math. Inequal. Appl. 23(4) (2020), 1205–1226.10.7153/mia-2020-23-93Suche in Google Scholar

[16] Edmunds, D. E.—Evans, W. D.: Spectral Theory and Differential Operators. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1987.Suche in Google Scholar

[17] Edmunds, D. E.—Evans, W. D.: Hardy Operators, Function Spaces and Embeddings, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2004.10.1007/978-3-662-07731-3Suche in Google Scholar

[18] Edmunds, D. E.—Triebel, H.: Sharp Sobolev embedding and related Hardy inequalities: the critical case, Math. Nachr. 207 (1999), 79–92.10.1002/mana.1999.3212070105Suche in Google Scholar

[19] Gesztesy, F.: On non-degenerate ground states for Schrödinger operators, Rep. Math. Phys. 20 (1984), 93–109.10.1016/0034-4877(84)90075-2Suche in Google Scholar

[20] Gesztesy, F.—Littlejohn, L. L.: Factorizations and Hardy-Rellich-type inequalities, Non-linear partial differential equations, mathematical physics, and stochastic analysis, 207–226, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2018.10.4171/186-1/10Suche in Google Scholar

[21] Gesztesy, F.—Mitrea, M.—Nenciu, I.—Teschl, G.: Decoupling of deficiency indices and applications to Schrödinger-type operators with possibly strongly singular potentials, Adv. Math. 301 (2016), 1022–1061.10.1016/j.aim.2016.08.008Suche in Google Scholar

[22] Gesztesy, F.—Ünal, M.: Perturbative oscillation criteria and Hardy-type inequalities, Math. Nachr. 189 (1998), 121–144.10.1002/mana.19981890108Suche in Google Scholar

[23] Ghoussoub, N.—Moradifam, A.: Bessel pairs and optimal Hardy and Hardy-Rellich inequalities, Math. Ann. 349 (2011), 1–57.10.1007/s00208-010-0510-xSuche in Google Scholar

[24] Ghoussoub, N.—Moradifam, A.: Functional Inequalities: New Perspectives and New Applications. Math. Surveys Monogr. 187, American Mathematical Society, Providence, RI, 2013.10.1090/surv/187Suche in Google Scholar

[25] Ioku, N.—Ishiwata, M.: A scale invariant form of a critical Hardy inequality, Int. Math. Res. Not. IMRN 18 (2015), 8830–8846.10.1093/imrn/rnu212Suche in Google Scholar

[26] Ioku, N.—Ishiwata, M.—Ozawa, T.: Sharp remainder of a critical Hardy inequality, Arch. Math. (Basel) 106(1) (2016), 65–71.10.1007/s00013-015-0841-7Suche in Google Scholar

[27] Kalf, H.—Walter, J.: Strongly singular potentials and essential self-adjointness of singular elliptic operators in C0∞(ℝⁿ ∖ {0}), J. Funct. Anal. 10 (1972), 114–130.10.1016/0022-1236(72)90059-6Suche in Google Scholar

[28] Kufner, A.—Maligranda, L.—Persson, L.-E.: The Hardy Inequality. About its History and Some Related Results, Vydavatelský Servis, Pilsen, 2007.Suche in Google Scholar

[29] Kufner, A.—Persson, L.-E.—Samko, N.: Weighted inequalities of Hardy type, 2nd ed., World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2017.10.1142/10052Suche in Google Scholar

[30] Lam, N.: A note on Hardy inequalities on homogeneous groups, Potential Anal. 51(3) (2019), 425–435.10.1007/s11118-018-9717-3Suche in Google Scholar

[31] Lam, N.: Hardy and Hardy-Rellich type inequalities with Bessel pairs, Ann. Acad. Sci. Fenn. Math. 43 (2018), 211–223.10.5186/aasfm.2018.4308Suche in Google Scholar

[32] Lam, N.—Lu, G.—Zhang, L.: Factorizations and Hardy’s type identities and inequalities on upper half spaces, Calc. Var. Partial Differential Equations 58(6) (2019), Art. ID 183.10.1007/s00526-019-1633-xSuche in Google Scholar

[33] Lam, N.—Lu, G.—Zhang, L.: Geometric Hardy’s inequalities with general distance functions, J. Funct. Anal. 279(8) (2020), Art. ID 108673.10.1016/j.jfa.2020.108673Suche in Google Scholar

[34] Leray, J.: Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l’Hydrodynamique, J. Math. Pures Appl. 12 (1933), 1–82.Suche in Google Scholar

[35] Machihara, S.—Ozawa, T.—Wadade, H.: Remarks on the Hardy type inequalities with remainder terms in the framework of equalities. Adv. Stud. Pure Math. 81, Asymptotic Analysis for Nonlinear Dispersive and Wave Equations, Mathematical Society of Japan, Tokyo, Japan, 2019, pp. 247–258.Suche in Google Scholar

[36] Maz’ya, V.: Sobolev Spaces with Applications to Elliptic Partial Differential Equations. Grundlehren Math. Wiss. 342 [Fundamental Principles of Mathematical Sciences], Second, revised and augmented edition, Springer, Heidelberg, 2011.Suche in Google Scholar

[37] Mercaldo, A.—Sano, M.—Takahashi, F.: Finsler Hardy inequalities, Math. Nachr. 293(12) (2020), 2370–2398.10.1002/mana.201900117Suche in Google Scholar

[38] Opic, B.—Kufner, A.: Hardy-type Inequalities, Research Notes in Mathematics Series 219, Pitman, Longman Scientific & Technical, Harlow, 1990.Suche in Google Scholar

[39] Rellich, F.: Perturbation Theory of Eigenvalue Problems, Gordon and Breach, New York, 1969.Suche in Google Scholar

[40] Russell, B.—Stepney, S.: Applications of Finsler geometry to speed limits to quantum information processing, Internat. J. Found. Comput. Sci. 25(4) (2014), 489–505.10.1142/S0129054114400073Suche in Google Scholar

[41] Ruzhansky, M.—Suragan, D.: A note on stability of Hardy inequalities, Ann. Funct. Anal. 9 (2018), 451-462.10.1215/20088752-2017-0060Suche in Google Scholar

[42] Ruzhansky, M.—Suragan, D.: Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups, Adv. Math. 317 (2017), 799–822.10.1016/j.aim.2017.07.020Suche in Google Scholar

[43] Ruzhansky, M.—Suragan, D.: Hardy Inequalities on Homogeneous Groups, Progress in Math. 327, Birkhäuser, 2019.10.1007/978-3-030-02895-4Suche in Google Scholar

[44] Sano, M.: Scaling invariant Hardy type inequalities with non-standard remainder terms, Math. Inequal. Appl. 21(1) (2018), 77–90.10.7153/mia-2018-21-06Suche in Google Scholar

[45] Sano, M.—Takahashi, F.: Scale invariance structures of the critical and the subcritical Hardy inequalities and their improvements, Calc. Var. Partial Differential Equations 56(3) (2017), Art. 69.10.1007/s00526-017-1166-0Suche in Google Scholar

[46] Sano, M.—Takahashi, F.: Sublinear eigenvalue problems with singular weights related to the critical Hardy inequality, Electron. J. Differential Equations (2016), Art. ID. 212.Suche in Google Scholar

[47] Schmincke, U-W.: Essential self-adjointness of a Schrödinger operator with strongly singular potential, Math. Z. 124 (1972), 47–50.10.1007/BF01142581Suche in Google Scholar

[48] Shen, Z.: Riemann-Finsler geometry with applications to information geometry, Chinese Ann. Math. Ser. B27(1) (2006), 73–94.10.1007/s11401-005-0333-3Suche in Google Scholar

[49] Van Schaftingen, J.: Anisotropic symmetrization, Ann. Inst. H. Poincaré Anal. Non Linéaire 23(4) (2006), 539–565.10.1016/j.anihpc.2005.06.001Suche in Google Scholar

[50] Wulff, G.: Zur Frage der Geschwindigkeit des Wachstums und der Auflösung der Kristallflzchen, Z. Kristallogr. 34 (1901), 449–530.10.1524/zkri.1901.34.1.449Suche in Google Scholar