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Selfadjointness of degenerate elliptic operators on higher order Sobolev spaces
Regular boundary value problems for ordinary differential-operator equations of higher order in UMD Banach spaces
1. | Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna |
2. | Raymond and Beverly Sackler School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel |
References:
[1] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, II, Comm. Pure Appl. Math., 12 (1959), 623-727; 17 (1964), 35-92. |
[2] |
W. Arendt and M. Duelli, Maximal $L^p$-regularity for parabolic and elliptic equations on the line, J. Evol. Equ., 6 (2006), 773-790.
doi: doi:10.1007/s00028-006-0292-5. |
[3] |
W. Arendt and A. F. M. ter Elst, Gaussian estimates for second order elliptic operators with boundary conditions, J. Operator Theory, 38 (1997), 87-130. |
[4] |
R. Denk, G. Dore, M. Hieber, J. Prüss and A. Venni, New thoughts on old results of R. T. Seeley, Mathematische Annalen, 328 (2004), 545-583.
doi: doi:10.1007/s00208-003-0493-y. |
[5] |
R. Denk, M. Hieber and J. Prüss, "$R$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type," Mem. Amer. Math. Soc., Providence, 2003. |
[6] |
A. Favini, V. Shakhmurov and Ya. Yakubov, Regular boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces, Semigroup Forum, 79 (2009), 22-54.
doi: doi:10.1007/s00233-009-9138-0. |
[7] |
A. Favini and Ya. Yakubov, Higher order ordinary differential-operator equations on the whole axis in UMD Banach spaces, Differential and Integral Equations, 21 (2008), 497-512. |
[8] |
A. Favini and Ya. Yakubov, Regular boundary value problems for elliptic differential-operator equations of the fourth order in UMD Banach spaces, Scientiae Mathematicae Japonicae, 70 (2009), 183-204. |
[9] |
A. Favini and Ya. Yakubov, Irregular boundary value problems for second order elliptic differential-operator equations in UMD Banach spaces, Mathematische Annalen, 348 (2010), 601-632.
doi: doi:10.1007/s00208-010-0491-9. |
[10] |
N. Kalton, P. Kunstmann and L. Weis, Perturbation and interpolation theorems for the $H^\infty$-calculus with applications to differential operators, Mathematische Annalen, 336 (2006), 747-801.
doi: doi:10.1007/s00208-005-0742-3. |
[11] |
N. Kalton and L. Weis, The $H^\infty$-calculus and sums of closed operators, Mathematische Annalen, 321 (2001), 319-345.
doi: doi:10.1007/s002080100231. |
[12] |
P. C. Kunstmann and L. Weis, "Maximal $L_p$-Regularity for Parabolic Equations, Fourier Multiplier Theorems and $H^\infty$-Functional Calculus," in "Functional Analytic Methods for Evolution Equations," Lecture Notes in Mathematics, 1855, Springer, (2004), 65-311. |
[13] |
H. Triebel, "Interpolation Theory. Function Spaces. Differential Operators," North-Holland, Amsterdam, 1978. |
[14] |
L. Weis, Operator-valued Fourier multiplier theorems and maximal $L_p$-regularity, Mathematische Annalen, 319 (2001), 735-758.
doi: doi:10.1007/PL00004457. |
[15] |
S. Yakubov and Ya. Yakubov, "Differential-Operator Equations. Ordinary and Partial Differential Equations," Chapman and Hall/CRC, Boca Raton, 2000. |
show all references
References:
[1] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, II, Comm. Pure Appl. Math., 12 (1959), 623-727; 17 (1964), 35-92. |
[2] |
W. Arendt and M. Duelli, Maximal $L^p$-regularity for parabolic and elliptic equations on the line, J. Evol. Equ., 6 (2006), 773-790.
doi: doi:10.1007/s00028-006-0292-5. |
[3] |
W. Arendt and A. F. M. ter Elst, Gaussian estimates for second order elliptic operators with boundary conditions, J. Operator Theory, 38 (1997), 87-130. |
[4] |
R. Denk, G. Dore, M. Hieber, J. Prüss and A. Venni, New thoughts on old results of R. T. Seeley, Mathematische Annalen, 328 (2004), 545-583.
doi: doi:10.1007/s00208-003-0493-y. |
[5] |
R. Denk, M. Hieber and J. Prüss, "$R$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type," Mem. Amer. Math. Soc., Providence, 2003. |
[6] |
A. Favini, V. Shakhmurov and Ya. Yakubov, Regular boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces, Semigroup Forum, 79 (2009), 22-54.
doi: doi:10.1007/s00233-009-9138-0. |
[7] |
A. Favini and Ya. Yakubov, Higher order ordinary differential-operator equations on the whole axis in UMD Banach spaces, Differential and Integral Equations, 21 (2008), 497-512. |
[8] |
A. Favini and Ya. Yakubov, Regular boundary value problems for elliptic differential-operator equations of the fourth order in UMD Banach spaces, Scientiae Mathematicae Japonicae, 70 (2009), 183-204. |
[9] |
A. Favini and Ya. Yakubov, Irregular boundary value problems for second order elliptic differential-operator equations in UMD Banach spaces, Mathematische Annalen, 348 (2010), 601-632.
doi: doi:10.1007/s00208-010-0491-9. |
[10] |
N. Kalton, P. Kunstmann and L. Weis, Perturbation and interpolation theorems for the $H^\infty$-calculus with applications to differential operators, Mathematische Annalen, 336 (2006), 747-801.
doi: doi:10.1007/s00208-005-0742-3. |
[11] |
N. Kalton and L. Weis, The $H^\infty$-calculus and sums of closed operators, Mathematische Annalen, 321 (2001), 319-345.
doi: doi:10.1007/s002080100231. |
[12] |
P. C. Kunstmann and L. Weis, "Maximal $L_p$-Regularity for Parabolic Equations, Fourier Multiplier Theorems and $H^\infty$-Functional Calculus," in "Functional Analytic Methods for Evolution Equations," Lecture Notes in Mathematics, 1855, Springer, (2004), 65-311. |
[13] |
H. Triebel, "Interpolation Theory. Function Spaces. Differential Operators," North-Holland, Amsterdam, 1978. |
[14] |
L. Weis, Operator-valued Fourier multiplier theorems and maximal $L_p$-regularity, Mathematische Annalen, 319 (2001), 735-758.
doi: doi:10.1007/PL00004457. |
[15] |
S. Yakubov and Ya. Yakubov, "Differential-Operator Equations. Ordinary and Partial Differential Equations," Chapman and Hall/CRC, Boca Raton, 2000. |
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