A global approach to fully nonlinear parabolic problems

Transactions of the American Mathematical Society

Volumn 352, Issue 10, 2000, Pages 4603-4640

  Kartsatos, Athanassios G ^a   Skrypnik, Igor V ^b  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

^b INSTITUTE OF APPLIED MATHEMATICS AND MECHANICS   (Ukraine)

Author keywords

Galerkin approximation. 2000 american mathematical society; Initial boundary value problem; Mapping of type (5)+; Skrypnik's degree theory for demicontinuous mappings of type (5)+

Indexed keywords

EID: 23044524071     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-00-02541-1     Document Type: Article

References (22)

1. P. Acquistapace and B. Terreni, Fully nonlinear parabolic systems, Recent Advances in Non-linear Elliptic and Parabolic Problems (Nancy, 1988), Pitman Res. Notes in Math., vol. 203, Longman Sei. Tech., Harlow, 1989, pp. 97-111. MR 92a:35080
2. H. Amann, Quasilincar parabolic systems under nonlinear boundary conditions, Arch. Rat. Mech. Anal. 92 (1986), 153-192. MR 87a:35101
3. G. C. Dong, Initial and oblique boundary value problems for fully nonlinear parabolic equations, J. Partial Differential Equations 1 (1988), 12-42. MR 90g:35073
4. S. I. Hudjaov, The first boundary value problem for nonlinear parabolic equations, Dokl. Akad. Nauk SSSR 149 (1963), 535-538;
5. English transi., Soviet Math. Dokl. 4 (1963), 441-445. MR 28:1404
6. V. P. Il'in, The properties of some classes of differentiable functions of several variables defined in an n-dimensional region, Trudy Mat. Inst. Stcklov 66 (1962), 227-363;
7. English transi., Amer. Math. Soc. Transi. (2) 81 (1969), 91-256. MR 27:3750
8. S. N. Kruzhkov, A. Castro and M. Lopcs, Schauder type estimates and theorems on the existence of the" solution of fundamental problem for linear and nonlinear parabolic equations, Dokl. Akad. Nauk SSSR 220 (1975), 277-280;
9. English transi., Soviet Math. Dokl. 16 (1975), 60-64. MR 52:14656
10. N. V. Krylov, Nonlinear elliptic and parabolic equations of the second order, Nauka, Moscow, 1985; English transi., Reidel, Dordrecht, 1987. MR 87h:35002; MR 88d:35005
11. O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, Linear and quasilinear equations of parabolic type, Nauka, Moscow, 1967; English transi., Amer. Math. Soc., Providence, RI, 1968. MR 39:3159a; MR 39:3159b
12. G. M. Lieberman, Second order parabolic differential equations, World Scientific, 1996, Singapore, 1996. MR 98k:35003
13. A. Lunardi, Maximal space regularity in nonhomogeneous parabolic problems, Numer. Punct. Anal. Optim. 10 (1989), 323-349. MR 90e:35093
14. A. Lunardi, On a class of fully nonlinear parabolic equations, Coram. Partial Differential Equations, 16 (1991), 145-172. MR 92c:35058
15. L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 115-162. MR 22:823
16. I. V. Skrypnik, Nonlinear higher order elliptic equations, Naukova Dumka, Kiev, 1973. (Russian) MR 55:8544
17. I. V. Skrypnik, Methods for analysis of nonlinear elliptic boundary value problems, Transi. Math. Monographs, vol. 139, Amer. Math. Soc., Providence, RI, 1994. MR 951:35109
18. V. A. Solonnikov, A priori estimates for second order parabolic equations, Trudy Mat. Inst. Steklov 70 (1964), 133-212;
19. English transi., Amer. Math. Soc. Transi. (2) 65 (1967), 51-137. MR 28:5267.
20. N. N. Sopolov, The first boundary value problem for nonlinear parabolic equations of any order, C. R. Acad. Bulgare Sei. 23 (1970), 899-902 (Russian). MR 51:1130
21. N. N. Uraltseva, A nonlinear broblem with an oblique derivative for a parabolic equation, 3. Math. Sei. 70 (1994), 1817-1827. MR 92d:35160 (Russian original)
22. L. Wang, On the regularity theory of fully nonlinear parabolic equations, Comm. Pure Appl. Math. 45 (1992), 27-76, 141-178. MR 92m:35126; MR 92m:35127