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An elliptic problem with degenerate coercivity and a singular quadratic gradient lower order term
An identity involving exterior derivatives and applications to Gaffney inequality
1. | Section de Mathématiques, EPFL, 1015 Lausanne, Switzerland |
2. | Section de Mathématiques, Station 8, EPFL, 1015 Lausanne |
References:
[1] | |
[2] |
G. Duvaut and J.-L. Lions, "Inequalities in Mechanics and Physics," Grundlehren der Mathematischen Wissenschaften, 219, Springer-Verlag, Berlin-New York, 1976. |
[3] |
M. P. Gaffney, The harmonic operator for exterior differential forms, Proc. Nat. Acad. of Sci. U. S. A., 37 (1951), 48-50. |
[4] |
M. P. Gaffney, Hilbert space methods in the theory of harmonic integrals, Trans. Amer. Math. Soc., 78 (1955), 426-444.
doi: 10.1090/S0002-9947-1955-0068888-1. |
[5] |
T. Iwaniec, C. Scott and B. Stroffolini, Nonlinear Hodge theory on manifolds with boundary, Ann. Mat. Pura Appl. (4), 177 (1999), 37-115.
doi: 10.1007/BF02505905. |
[6] |
S. G. Krantz and H. R. Parks, "The Geometry of Domains in Space," Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser Boston, Inc., Boston, 1999. |
[7] |
C. B. Morrey, Jr., A variational method in the theory of harmonic integrals II, Amer. J. Math., 78 (1956), 137-170.
doi: 10.2307/2372488. |
[8] |
C. B. Morrey, Jr., "Multiple Integrals in the Calculus of Variations," Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag, New-York, 1966. |
[9] |
G. Schwarz, "Hodge Decomposition-A Method for Solving Boundary Value Problems," Lecture Notes in Math., 1607, Springer-Verlag, Berlin, 1995. |
show all references
References:
[1] | |
[2] |
G. Duvaut and J.-L. Lions, "Inequalities in Mechanics and Physics," Grundlehren der Mathematischen Wissenschaften, 219, Springer-Verlag, Berlin-New York, 1976. |
[3] |
M. P. Gaffney, The harmonic operator for exterior differential forms, Proc. Nat. Acad. of Sci. U. S. A., 37 (1951), 48-50. |
[4] |
M. P. Gaffney, Hilbert space methods in the theory of harmonic integrals, Trans. Amer. Math. Soc., 78 (1955), 426-444.
doi: 10.1090/S0002-9947-1955-0068888-1. |
[5] |
T. Iwaniec, C. Scott and B. Stroffolini, Nonlinear Hodge theory on manifolds with boundary, Ann. Mat. Pura Appl. (4), 177 (1999), 37-115.
doi: 10.1007/BF02505905. |
[6] |
S. G. Krantz and H. R. Parks, "The Geometry of Domains in Space," Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser Boston, Inc., Boston, 1999. |
[7] |
C. B. Morrey, Jr., A variational method in the theory of harmonic integrals II, Amer. J. Math., 78 (1956), 137-170.
doi: 10.2307/2372488. |
[8] |
C. B. Morrey, Jr., "Multiple Integrals in the Calculus of Variations," Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag, New-York, 1966. |
[9] |
G. Schwarz, "Hodge Decomposition-A Method for Solving Boundary Value Problems," Lecture Notes in Math., 1607, Springer-Verlag, Berlin, 1995. |
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