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On the regularity up to the boundary for certain nonlinear elliptic systems
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Elliptic boundary value problems in spaces of continuous functions
1. | Dipartimento di Matematica Applicata, Università di Pisa, Via Buonarroti 1/C, 56127 Pisa |
References:
[1] |
H. Beirão da Veiga, On the solutions in the large of the two-dimensional flow of a nonviscous incompressible fluid, J. Diff. Eq., 54 (1984), 373-389.
doi: 10.1016/0022-0396(84)90149-9. |
[2] |
H. Beirão da Veiga, Concerning the existence of classical solutions to the Stokes system. On the minimal assumptions problem, J. Math. Fluid Mech., 16 (2014), 539-550.
doi: 10.1007/s00021-014-0170-9. |
[3] |
H. Beirão da Veiga, An overview on classical solutions to $2-D$ Euler equations and to elliptic boundary value problems,, in Recent Progress in the Theory of the Euler and Navier-Stokes Equations (eds. J. C. Robinson, ().
|
[4] |
H. Beirão da Veiga, On some regularity results for the stationary Stokes system and the $2-D$ Euler equations, Portugaliae Math., 72 (2015), 285-307.
doi: 10.4171/PM/1969. |
[5] |
H. Beirão da Veiga, H-log spaces of continuous functions, potentials, and elliptic boundary value problems, arXiv:1503.04173, 2015. |
[6] |
L. Bers, F. John and M. Schechter, Partial Differential Equations, John Wiley and Sons, Inc., New-York, 1964. |
[7] |
C. C. Burch, The Dini condition and regularity of weak solutions of elliptic equations, J. Diff. Eq., 30 (1978), 308-323.
doi: 10.1016/0022-0396(78)90003-7. |
[8] |
D. V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces Foundations and Harmonic Analysis, Springer, Basel 2013.
doi: 10.1007/978-3-0348-0548-3. |
[9] |
O. A. Ladyzenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New-York, 1969. |
[10] |
V. L. Shapiro, Generalized and classical solutions of the nonlinear stationary Navier-Stokes equations, Trans. Amer. Math. Soc., 216 (1976), 61-79.
doi: 10.1090/S0002-9947-1976-0390550-X. |
[11] |
I. I. Sharapudinov, The basis property of the Haar system in the space $L^{p(t)}[0,1]$, and the principle of localization in the mean, Mat. Sb. (N.S.), 130 (1986), 275-283, 286. |
[12] |
V. A. Solonnikov, On estimates of Green's tensors for certain boundary value problems, Doklady Akad. Nauk., 130 (1960), 128-131. |
show all references
References:
[1] |
H. Beirão da Veiga, On the solutions in the large of the two-dimensional flow of a nonviscous incompressible fluid, J. Diff. Eq., 54 (1984), 373-389.
doi: 10.1016/0022-0396(84)90149-9. |
[2] |
H. Beirão da Veiga, Concerning the existence of classical solutions to the Stokes system. On the minimal assumptions problem, J. Math. Fluid Mech., 16 (2014), 539-550.
doi: 10.1007/s00021-014-0170-9. |
[3] |
H. Beirão da Veiga, An overview on classical solutions to $2-D$ Euler equations and to elliptic boundary value problems,, in Recent Progress in the Theory of the Euler and Navier-Stokes Equations (eds. J. C. Robinson, ().
|
[4] |
H. Beirão da Veiga, On some regularity results for the stationary Stokes system and the $2-D$ Euler equations, Portugaliae Math., 72 (2015), 285-307.
doi: 10.4171/PM/1969. |
[5] |
H. Beirão da Veiga, H-log spaces of continuous functions, potentials, and elliptic boundary value problems, arXiv:1503.04173, 2015. |
[6] |
L. Bers, F. John and M. Schechter, Partial Differential Equations, John Wiley and Sons, Inc., New-York, 1964. |
[7] |
C. C. Burch, The Dini condition and regularity of weak solutions of elliptic equations, J. Diff. Eq., 30 (1978), 308-323.
doi: 10.1016/0022-0396(78)90003-7. |
[8] |
D. V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces Foundations and Harmonic Analysis, Springer, Basel 2013.
doi: 10.1007/978-3-0348-0548-3. |
[9] |
O. A. Ladyzenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New-York, 1969. |
[10] |
V. L. Shapiro, Generalized and classical solutions of the nonlinear stationary Navier-Stokes equations, Trans. Amer. Math. Soc., 216 (1976), 61-79.
doi: 10.1090/S0002-9947-1976-0390550-X. |
[11] |
I. I. Sharapudinov, The basis property of the Haar system in the space $L^{p(t)}[0,1]$, and the principle of localization in the mean, Mat. Sb. (N.S.), 130 (1986), 275-283, 286. |
[12] |
V. A. Solonnikov, On estimates of Green's tensors for certain boundary value problems, Doklady Akad. Nauk., 130 (1960), 128-131. |
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