Time-periodic solutions of quasilinear parabolic differential equations II. Oblique derivative boundary conditions

 Access to full text

 Full (PDF)

1. [1] H. Amann, Periodic solutions of semi-linear parabolic equations, in: Non-linear Analysis: A Collection of Papers in Honor of Erich H. Rothe (L. Cesari, R. Kannan, H. Weinberger, eds.), Academic Press, New York 1978, 1-29. 
2. [5] G. C. Dong, Initial and nonlinear oblique boundary value problems for fully nonlinear parabolic equations, J. Partial Differential Equations 1 (1988), 12-42. Zbl0699.35152
3. [6] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Second Edition, Springer-Verlag, Berlin-Heidelberg-New York, 1983. Zbl0562.35001
4. [7] P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, Longman Scientific & Technical, Harlow, Essex, 1991. Zbl0731.35050
5. [Kli] V. S. Klimov, Periodic and stationary solutions of quasilinear parabolic equations, Sib. Mat. Zh. 17 (1976), 530-532 [Russian]; English transl. in Sib. Math. J. 17 (1976), 530-533. 
6. [9] S. N. Kruzhkov, Periodic solutions to nonlinear equations, Differentsial'nye Uravneniya 6 (1970), 731-740 [Russian]; English transl. in Differential Equations 6 (1970), 560-566. 
7. [10] O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R. I. 1968. 
8. [13] G. M. Lieberman, The nonlinear oblique derivative problem for quasilinear elliptic equations, Nonlinear Anal. 8 (1984) 49-65. Zbl0541.35032
9. [14] G. M. Lieberman, Solvability of quasilinear elliptic equations with nonlinear boundary conditions. II, J. Functional Anal. 56 (1984), 210-219. Zbl0538.35035
10. [17] G. M. Lieberman, Intermediate Schauder theory for second order parabolic equations IV. Time irregularity and regularity, Differential Integral Equations 5 (1992), 1219-1236. Zbl0785.35047
11. [20] G. M. Lieberman, Second Order Parabolic Differential Equations, World Scientific, Singapore, 1996. Zbl0884.35001
12. [21] G. M. Lieberman, Time-periodic solutions of linear parabolic differential equations, Comm. Partial Differential Equations 24 (1999), 631-663. Zbl0928.35012
13. [22] G. M. Lieberman, Time-periodic solutions of quasilinear parabolic differential equations I. Dirichlet boundary conditions, (to appear). Zbl1002.35073
14. [23] G. M. Lieberman and N. S. Trudinger, Nonlinear oblique boundary value problems for fully nonlinear elliptic equations, Trans. Amer. Math. Soc. 295 (1986), 509-546. Zbl0619.35047
15. [25] M. N. Nkashama, Semilinear periodic-parabolic equations with nonlinear boundary conditions, J. Differential Equations 130 (1996), 377-405. 
16. [26] I. I. Šmulev, Periodic solutions of the first boundary value problem for parabolic equations, Mat. Sb. 66 (1965), 398-410 [Russian]; English transl. in Amer. Math. Soc. Transl. 79 (1969), 215-229. 
17. [27] I. I. Šmulev, Quasi-periodic and periodic solutions of the problem with oblique derivative for parabolic equations, Differentsial'nye Uravneniya 5 (1969), 2225-2236 [Russian]; English transl. in Differential Equations 5 (1969), 2668-1676. 
18. [28] N. S. Trudinger, On an interpolation inequality and its application to nonlinear elliptic equations, Proc. Amer. Math. Soc. 95 (1985), 73-78. Zbl0579.35029
19. [30] N. N. Ural'tseva, Gradient estimates for solutions of nonlinear parabolic oblique boundary problems, Contemp. Math. 127 (1992), 119-130. Zbl0770.35034
20. [31] O. Vejvoda, Partial differential equations: time-periodic solutions, Martinus Nijhoff, The Hague/ Boston/ London, 1982.