On the natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva
Lieberman, Gary
Banach Center Publications, Tome 27 (1992), p. 295-308 / Harvested from The Polish Digital Mathematics Library
Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:262650
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     author = {Lieberman, Gary},
     title = {On the natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva},
     journal = {Banach Center Publications},
     volume = {27},
     year = {1992},
     pages = {295-308},
     zbl = {0802.35040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z2p295bwm}
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Lieberman, Gary. On the natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva. Banach Center Publications, Tome 27 (1992) pp. 295-308. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z2p295bwm/

[000] [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. | Zbl 0711.49058

[001] [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. | Zbl 0733.35024

[002] [3] H. J. Choe, Regularity for certain degenerate elliptic double obstacle problems, J. Math. Anal. Appl., to appear. | Zbl 0798.35057

[003] [4] E. DiBenedetto, C1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983), 827-850. | Zbl 0539.35027

[004] [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. | Zbl 0635.35052

[005] [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. | Zbl 0673.35047

[006] [7] E. DiBenedetto and Y.-Z. Chen, Boundary estimates for solutions of nonlinear degenerate parabolic systems, J. Reine Angew. Math. 395 (1989), 102-131. | Zbl 0661.35052

[007] [8] E. DiBenedetto and A. Friedman, Regularity of solutions of nonlinear degenerate parabolic systems, ibid. 349 (1984), 83-128. | Zbl 0527.35038

[008] [9] E. DiBenedetto and A. Friedman, Hölder estimates for nonlinear degenerate parabolic systems, ibid. 357 (1985), 1-22. | Zbl 0549.35061

[009] [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. | Zbl 0726.35066

[010] [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. | Zbl 0565.35012

[011] [12] T. K. Donaldson and N. S. Trudinger, Orlicz-Sobolev spaces and imbedding theorems, J. Funct. Anal. 8 (1971), 52-75. | Zbl 0216.15702

[012] [13] M. Giaquinta, Growth conditions and regularity, a counterexample, Manuscripta Math. 59 (1987), 245-248. | Zbl 0638.49005

[013] [14] M. Giaquinta and E. Giusti, Global C1,α regularity for second order quasilinear elliptic equations in divergence form, J. Reine Angew. Math. 351 (1984), 55-65. | Zbl 0528.35014

[014] [15] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, Berlin 1983. | Zbl 0562.35001

[015] [16] T. Kilpeläinen and W. P. Ziemer, Pointwise regularity of solutions to nonlinear double obstacle problems, Ark. Mat. 29 (1991), 83-106. | Zbl 0733.35025

[016] [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.

[017] [18] M. A. Kranosel'skii and Ya. B. Rutickii, Convex Functions and Orlicz Spaces, Noordhoff, Groningen 1961.

[018] [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.

[019] [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.

[020] [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.

[021] [22] G. M. Lieberman, Interior gradient bounds for non-uniformly parabolic equations, Indiana Univ. Math. J. 32 (1983), 579-601. | Zbl 0491.35021

[022] [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. | Zbl 0655.35047

[023] [24] G. M. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. 12 (1988), 1203-1219. | Zbl 0675.35042

[024] [25] G. M. Lieberman, Boundary regularity for solutions of degenerate parabolic equations, ibid. 14 (1990), 501-524. | Zbl 0703.35098

[025] [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. | Zbl 0742.35028

[026] [27] G. M. Lieberman, Local and boundary regularity for some variational inequalities involving p-Laplaciantype operators, to appear.

[027] [28] G. M. Lieberman, Regularity of solutions to some degenerate double obstacle problems, Indiana Univ. Math. J. 40 (1991), 1009-1028. | Zbl 0767.35029

[028] [29] G. M. Lieberman, Boundary and initial regularity for solutions of degenerate parabolic equations, Nonlinear Anal., to appear. | Zbl 0782.35036

[029] [30] J. H. Michael and W. P. Ziemer, Interior regularity for solutions to obstacle problems, Nonlinear Anal. 10 (1986), 1427-1448. | Zbl 0603.49006

[030] [31] J. H. Michael and W. P. Ziemer, Existence of solutions to obstacle problems, ibid. 17 (1991), 45-71. | Zbl 0735.35067

[031] [32] J. Mu, Higher regularity of the solution to the p-Laplacian obstacle problem, J. Differential Equations 95 (1992), 370-384. | Zbl 0765.49008

[032] [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. | Zbl 0742.35010

[033] [34] L. M. Simon, Interior gradient bounds for non-uniformly elliptic equations, Indiana Univ. Math. J. 25 (1976), 821-855. | Zbl 0346.35016

[034] [35] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984), 126-150. | Zbl 0488.35017

[035] [36] K. Uhlenbeck, Regularity for a class of non-linear elliptic systems, Acta Math. 138 (1977), 219-240. | Zbl 0372.35030

[036] [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.

[037] [38] M. Wiegner, On Cα-regularity of the gradient of solutions of degenerate parabolic systems, Ann. Mat. Pura Appl. 145 (1986), 385-405. | Zbl 0642.35046