Best constants for higher-order Rellich inequalities in L p (Ω)

Mathematische Zeitschrift

Volumn 255, Issue 4, 2007, Pages 877-896

  Barbatis, G ^a  

^a UNIVERSITY OF IOANNINA   (Greece)

Author keywords

Best constants; Distance function; Rellich inequality

Indexed keywords

EID: 33846560999     PISSN: 00255874     EISSN: 14321823     Source Type: Journal    
DOI: 10.1007/s00209-006-0056-5     Document Type: Article

References (12)

1. 1,p and its application to Schrödinger operators. NoDEA. Nonlinear Diff. Equal. Appl. 12, 243-263 (2005)
2. Ambrosio, L., Soner, H.M.: Level set approach to mean curvature flow in arbitrary codimension. J. Diff. Geometry 43, 693-737 (1996)
3. Barbatis, G.: Improved Rellich inequalities for the polyharmonic operator. Indiana Univ. Math. J. 55, 1401-1422 (2006)
4. P Hardy inequality. Indiana Univ. Math. J. 52, 171-190 (2003)
5. Barbatis, G., Tertikas, A.: On a class of Rellich inequalities. J. Corap. Appl. Math. 194, 156-172 (2006)
6. Brezis, H., Vázquez, J.-L.: Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Comp. Madrid 10, 443-469 (1997)
7. P(Ω). Math. Z. 227, 511-523 (1998)
8. Galaktionov, V.: On extensions of higher-order Hardy's inequalities. Diff. Equat. 19, 327-344 (2006)
9. Gazzola, F., Grunau, H.-Ch., Mitidieri, E.: Hardy inequalities with optimal constants and remainder terms. Trans. Am. Math. Soc. 356, 2149-2168 (2004)
10. Schoen, R., Yau, S.-T.: Lectures in Differential Geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, I., International Press, Somerislle (1994)
11. Tertikas, A., Zographopoulos, N.: Best constants in the Hardy-Rellich inequalities and related improvements. Adv. Math, (to appear)
12. P Hardy inequalities in general domains. Stockholm University Ph.D. Thesis, 2003. Available at www.math.su.se/reports/ 2003/4/