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On a class of elliptic operators with unbounded diffusion coefficients
1. | Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento, C.P.193, 73100, Lecce |
2. | Dipartimento di Matematica e Fisica "Ennio De Giorgi", Università del Salento, C.P.193, 73100, Lecce, Italy |
References:
[1] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, Comm. on Pure and Appl. Math., 12 (1959), 623-727.
doi: 10.1002/cpa.3160120405. |
[2] |
G. Cupini and S. Fornaro, Maximal regularity in $L^p$ for a class of elliptic operators with unbounded coefficients, Diff. Int. Eqs., 17 (2004), 259-296. |
[3] |
S. Fornaro and L. Lorenzi, Generation results for elliptic operators with unbounded diffusion coefficients in $L^p$ and $C_b$-spaces, Discrete and continuous dynamical sistems, 18 (2007), 747-772.
doi: 10.3934/dcds.2007.18.747. |
[4] |
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Second edition, Springer, Berlin, 1983.
doi: 10.1007/978-3-642-61798-0. |
[5] |
P. G. Galdi, G. Metafune, C. Spina and C. Tacelli, Homogeneous Calderón-Zygmund estimates for a class of second order elliptic operators, Communications in contemporary mathematics, (2014), online available.
doi: 10.1142/S0219199714500175. |
[6] |
G. Metafune and C. Spina, Elliptic operators with unbounded coefficients in $L^p$ spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci., 11 (2012), 303-340. |
[7] |
G. Metafune and C. Spina, Kernel estimates for some elliptic operators with unbounded coefficients, DCDS-A, 32 (2012), 2285-2299.
doi: 10.3934/dcds.2012.32.2285. |
[8] |
G. Metafune and C. Spina, A degenerate elliptic operator with unbounded diffusion coefficients, Rendiconti dell'accademia Nazionale dei Lincei, 25 (2014), 109-140.
doi: 10.4171/RLM/670. |
[9] |
G. Metafune, C. Spina and C. Tacelli, Elliptic operators with unbounded diffusion and drift coefficients in $L^p$ spaces, Advances in Differential Equations, 19 (2014), 473-526. |
[10] |
G. Metafune, D. Pallara and M. Wacker, Feller Semigroups on $\mathbb{R}^N2$, Semigroup Forum, 65 (2002), 159-205.
doi: 10.1007/s002330010129. |
[11] |
C. Spina, Kernel estimates for some elliptic elliptic operators with unbounded diffusion coefficients in the one-dimensional and bi-dimensional cases, Semigroup Forum, 86 (2013), 67-82.
doi: 10.1007/s00233-012-9420-4. |
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, Comm. on Pure and Appl. Math., 12 (1959), 623-727.
doi: 10.1002/cpa.3160120405. |
[2] |
G. Cupini and S. Fornaro, Maximal regularity in $L^p$ for a class of elliptic operators with unbounded coefficients, Diff. Int. Eqs., 17 (2004), 259-296. |
[3] |
S. Fornaro and L. Lorenzi, Generation results for elliptic operators with unbounded diffusion coefficients in $L^p$ and $C_b$-spaces, Discrete and continuous dynamical sistems, 18 (2007), 747-772.
doi: 10.3934/dcds.2007.18.747. |
[4] |
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Second edition, Springer, Berlin, 1983.
doi: 10.1007/978-3-642-61798-0. |
[5] |
P. G. Galdi, G. Metafune, C. Spina and C. Tacelli, Homogeneous Calderón-Zygmund estimates for a class of second order elliptic operators, Communications in contemporary mathematics, (2014), online available.
doi: 10.1142/S0219199714500175. |
[6] |
G. Metafune and C. Spina, Elliptic operators with unbounded coefficients in $L^p$ spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci., 11 (2012), 303-340. |
[7] |
G. Metafune and C. Spina, Kernel estimates for some elliptic operators with unbounded coefficients, DCDS-A, 32 (2012), 2285-2299.
doi: 10.3934/dcds.2012.32.2285. |
[8] |
G. Metafune and C. Spina, A degenerate elliptic operator with unbounded diffusion coefficients, Rendiconti dell'accademia Nazionale dei Lincei, 25 (2014), 109-140.
doi: 10.4171/RLM/670. |
[9] |
G. Metafune, C. Spina and C. Tacelli, Elliptic operators with unbounded diffusion and drift coefficients in $L^p$ spaces, Advances in Differential Equations, 19 (2014), 473-526. |
[10] |
G. Metafune, D. Pallara and M. Wacker, Feller Semigroups on $\mathbb{R}^N2$, Semigroup Forum, 65 (2002), 159-205.
doi: 10.1007/s002330010129. |
[11] |
C. Spina, Kernel estimates for some elliptic elliptic operators with unbounded diffusion coefficients in the one-dimensional and bi-dimensional cases, Semigroup Forum, 86 (2013), 67-82.
doi: 10.1007/s00233-012-9420-4. |
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