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On the threshold for Kato's selfadjointness problem and its $L^p$-generalization
1. | Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, Japan |
References:
[1] |
E. B. Davies, $L^{1}$ properties of second order elliptic operators,, Bull. London Math. Soc., 17 (1985), 417.
doi: 10.1112/blms/17.5.417. |
[2] |
A. Devinatz, Essential self-adjointness of Schrödinger-type operators,, J. Functional Analysis, 25 (1977), 58.
doi: 10.1016/0022-1236(77)90032-5. |
[3] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order,, Revised Third Printing, (1998).
|
[4] |
D. M. Gitman, I. V. Tyutin and B. L. Voronov, Self-adjoint Extensions in Quantum Mechanics, General Theory and Applications to Schrodinger and Dirac Equations with Singular Potentials,, Progress in Mathematical Physics 62, 62 (2012).
doi: 10.1007/978-0-8176-4662-2. |
[5] |
T. Kato, Remarks on the selfadjointness and related problems for differential operators,, Spectral theory of differential operators (Birmingham, 55 (1981), 253.
doi: 10.1016/S0304-0208(08)71641-4. |
[6] |
G. Metafune, N. Okazawa, M. Sobajima and C. Spina, Scale invariant elliptic operators with singular coefficients,, preprint, (). Google Scholar |
[7] |
G. Metafune, D. Pallara, P. J. Rabier and R. Schnaubelt, Uniqueness for elliptic operators on $L^p(\mathbbR^N)$ with unbounded coefficients,, Forum Math., 22 (2010), 583.
doi: 10.1515/forum.2010.031. |
[8] |
G. Metafune and C. Spina, Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces,, Ann. Sc. Norm. Super. Pisa Cl. Sci., 11 (2012), 303.
doi: 10.2422/2036-2145.201010_012. |
[9] |
N. Okazawa, Sectorialness of second order elliptic operators in divergence form,, Proc. Amer. Math. Soc., 113 (1991), 701.
doi: 10.1090/S0002-9939-1991-1072347-4. |
[10] |
B. Simon, Schrödinger semigroups,, Bull. Amer. Math. Soc. (N.S.), 7 (1982), 447.
doi: 10.1090/S0273-0979-1982-15041-8. |
[11] |
M. Sobajima, $L^p$-theory for second-order elliptic operators with unbounded coefficients,, J. Evol. Equ., 12 (2012), 957.
doi: 10.1007/s00028-012-0163-1. |
[12] |
M. Sobajima, $L^p$-theory for second-order elliptic operators with unbounded coefficients in an endpoint class,, J. Evol. Equ., 14 (2014), 461.
doi: 10.1007/s00028-014-0223-9. |
show all references
References:
[1] |
E. B. Davies, $L^{1}$ properties of second order elliptic operators,, Bull. London Math. Soc., 17 (1985), 417.
doi: 10.1112/blms/17.5.417. |
[2] |
A. Devinatz, Essential self-adjointness of Schrödinger-type operators,, J. Functional Analysis, 25 (1977), 58.
doi: 10.1016/0022-1236(77)90032-5. |
[3] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order,, Revised Third Printing, (1998).
|
[4] |
D. M. Gitman, I. V. Tyutin and B. L. Voronov, Self-adjoint Extensions in Quantum Mechanics, General Theory and Applications to Schrodinger and Dirac Equations with Singular Potentials,, Progress in Mathematical Physics 62, 62 (2012).
doi: 10.1007/978-0-8176-4662-2. |
[5] |
T. Kato, Remarks on the selfadjointness and related problems for differential operators,, Spectral theory of differential operators (Birmingham, 55 (1981), 253.
doi: 10.1016/S0304-0208(08)71641-4. |
[6] |
G. Metafune, N. Okazawa, M. Sobajima and C. Spina, Scale invariant elliptic operators with singular coefficients,, preprint, (). Google Scholar |
[7] |
G. Metafune, D. Pallara, P. J. Rabier and R. Schnaubelt, Uniqueness for elliptic operators on $L^p(\mathbbR^N)$ with unbounded coefficients,, Forum Math., 22 (2010), 583.
doi: 10.1515/forum.2010.031. |
[8] |
G. Metafune and C. Spina, Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces,, Ann. Sc. Norm. Super. Pisa Cl. Sci., 11 (2012), 303.
doi: 10.2422/2036-2145.201010_012. |
[9] |
N. Okazawa, Sectorialness of second order elliptic operators in divergence form,, Proc. Amer. Math. Soc., 113 (1991), 701.
doi: 10.1090/S0002-9939-1991-1072347-4. |
[10] |
B. Simon, Schrödinger semigroups,, Bull. Amer. Math. Soc. (N.S.), 7 (1982), 447.
doi: 10.1090/S0273-0979-1982-15041-8. |
[11] |
M. Sobajima, $L^p$-theory for second-order elliptic operators with unbounded coefficients,, J. Evol. Equ., 12 (2012), 957.
doi: 10.1007/s00028-012-0163-1. |
[12] |
M. Sobajima, $L^p$-theory for second-order elliptic operators with unbounded coefficients in an endpoint class,, J. Evol. Equ., 14 (2014), 461.
doi: 10.1007/s00028-014-0223-9. |
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