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## Banach Center Publications

1992 | 27 | 2 | 295-308
Tytuł artykułu

### On the natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
295-308
Opis fizyczny
Daty
wydano
1992
Twórcy
autor
• Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA
Bibliografia
• [1] L. Boccardo, P. Marcellini and C. Sbordone, $L^∞$-regularity for variational problems with sharp non standard growth conditions, Boll. Un. Mat. Ital. (7) 4-A (1990), 219-225.
• [2] H. J. Choe, A regularity theory for a more general class of quasilinear elliptic differential equations and obstacle problems, Arch. Rational Mech. Anal. 114 (1991), 393-394.
• [3] H. J. Choe, Regularity for certain degenerate elliptic double obstacle problems, J. Math. Anal. Appl., to appear.
• [4] E. DiBenedetto, $C^{1+α}$ local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983), 827-850.
• [5] E. DiBenedetto, On the local behavior of solutions of degenerate parabolic equations with measurable coefficients, Ann. Scuola Norm. Sup. Pisa (4) 13 (1986), 487-535.
• [6] E. DiBenedetto and Y.-Z. Chen, On the local behaviour of solutions of singular parabolic equations, Arch. Rational Mech. Anal. 103 (1988), 319-345.
• [7] E. DiBenedetto and Y.-Z. Chen, Boundary estimates for solutions of nonlinear degenerate parabolic systems, J. Reine Angew. Math. 395 (1989), 102-131.
• [8] E. DiBenedetto and A. Friedman, Regularity of solutions of nonlinear degenerate parabolic systems, ibid. 349 (1984), 83-128.
• [9] E. DiBenedetto and A. Friedman, Hölder estimates for nonlinear degenerate parabolic systems, ibid. 357 (1985), 1-22.
• [10] E. DiBenedetto and M. A. Herrero, Non-negative solutions of the evolution p-Laplacian equation. Initial traces and Cauchy problem when 1 < p < 2, Arch. Rational Mech. Anal. 111 (1990), 225-290.
• [11] E. DiBenedetto and N. S. Trudinger, Harnack inequalities for quasi-minima of variational integrals, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), 295-308.
• [12] T. K. Donaldson and N. S. Trudinger, Orlicz-Sobolev spaces and imbedding theorems, J. Funct. Anal. 8 (1971), 52-75.
• [13] M. Giaquinta, Growth conditions and regularity, a counterexample, Manuscripta Math. 59 (1987), 245-248.
• [14] M. Giaquinta and E. Giusti, Global $C^{1,α}$ regularity for second order quasilinear elliptic equations in divergence form, J. Reine Angew. Math. 351 (1984), 55-65.
• [15] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, Berlin 1983.
• [16] T. Kilpeläinen and W. P. Ziemer, Pointwise regularity of solutions to nonlinear double obstacle problems, Ark. Mat. 29 (1991), 83-106.
• [17] A. G. Korolev, On boundedness of generalized solutions of elliptic differential equations with nonpower nonlinearities, Mat. Sb. 180 (1989), 78-100 (in Russian); English transl.: Math. USSR-Sb. 66 (1990), 83-106.
• [18] M. A. Kranosel'skii and Ya. B. Rutickii, Convex Functions and Orlicz Spaces, Noordhoff, Groningen 1961.
• [19] N. V. Krylov, Boundedly nonhomogeneous elliptic and parabolic equations in a domain, Izv. Akad. Nauk SSSR Ser. Mat. 47 (1983), 75-108 (in Russian); English transl.: Math. USSR-Izv. 21 (1984), 67-98.
• [20] O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1967.
• [21] O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Nauka, Moscow 1964 (in Russian); English transl.: Academic Press, New York 1968. 2nd Russian ed., 1973.
• [22] G. M. Lieberman, Interior gradient bounds for non-uniformly parabolic equations, Indiana Univ. Math. J. 32 (1983), 579-601.
• [23] G. M. Lieberman, The first initial-boundary value problem for quasilinear second order parabolic equations, Ann. Scuola Norm Sup. Pisa (4) 13 (1986), 347-387.
• [24] G. M. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. 12 (1988), 1203-1219.
• [25] G. M. Lieberman, Boundary regularity for solutions of degenerate parabolic equations, ibid. 14 (1990), 501-524.
• [26] G. M. Lieberman, The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations, Comm. Partial Differential Equations 16 (1991), 311-361.
• [27] G. M. Lieberman, Local and boundary regularity for some variational inequalities involving p-Laplaciantype operators, to appear.
• [28] G. M. Lieberman, Regularity of solutions to some degenerate double obstacle problems, Indiana Univ. Math. J. 40 (1991), 1009-1028.
• [29] G. M. Lieberman, Boundary and initial regularity for solutions of degenerate parabolic equations, Nonlinear Anal., to appear.
• [30] J. H. Michael and W. P. Ziemer, Interior regularity for solutions to obstacle problems, Nonlinear Anal. 10 (1986), 1427-1448.
• [31] J. H. Michael and W. P. Ziemer, Existence of solutions to obstacle problems, ibid. 17 (1991), 45-71.
• [32] J. Mu, Higher regularity of the solution to the p-Laplacian obstacle problem, J. Differential Equations 95 (1992), 370-384.
• [33] J. Mu and W. P. Ziemer, Smooth regularity of solutions of double obstacle problems involving degenerate elliptic equations, Comm. Partial Differential Equations 16 (1991), 821-843.
• [34] L. M. Simon, Interior gradient bounds for non-uniformly elliptic equations, Indiana Univ. Math. J. 25 (1976), 821-855.
• [35] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984), 126-150.
• [36] K. Uhlenbeck, Regularity for a class of non-linear elliptic systems, Acta Math. 138 (1977), 219-240.
• [37] N. N. Ural'tseva, Degenerate quasilinear elliptic systems, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 7 (1968), 184-222 (in Russian); English transl.: Sem. Math. V. A. Steklov Math. Inst. Leningrad 7 (1968), 83-99.
• [38] M. Wiegner, On $C_α$-regularity of the gradient of solutions of degenerate parabolic systems, Ann. Mat. Pura Appl. 145 (1986), 385-405.
Typ dokumentu
Bibliografia
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