Quasilinear parabolic operators with discontinuous ingredients

Acquistapace, 1992, On BMO regularity for linear elliptic systems, Ann. Mat. Pura Appl., 161, 231, 10.1007/BF01759640 Amann, 1978, On some existence theorems for semi-linear elliptic equations, Indiana Univ. Math. J., 27, 779, 10.1512/iumj.1978.27.27050 Bramanti, 1993, Wp1,2 solvability for the Cauchy–Dirichlet problem for parabolic equations with VMO coefficients, Comm. Partial Differential Equations, 18, 1735, 10.1080/03605309308820991 F. Chiarenza, Lp regularity for systems of PDE's with coefficients in VMO, in: Nonlinear Analysis, Function Spaces and Applications, Vol. 5, Prague, 1994, http://www.emis.de/proceedings/Praha94/3.html. Chiarenza, 1991, Interior W2,p estimates for nondivergence elliptic equations with discontinuous coefficients, Ricerche Mat., 40, 149 Chiarenza, 1993, W2,p solvability of the Dirichlet problem for nondivergence form elliptic equations with VMO coefficients, Trans. Amer. Math. Soc., 336, 841, 10.2307/2154379 Di Fazio, 1996, Oblique derivative problem for quasilinear elliptic equations with VMO coefficients, Bull. Austral. Math. Soc., 53, 501, 10.1017/S0004972700017275 Fučik, 1980 Gilbarg, 1983 John, 1961, On functions of bounded mean oscillation, Comm. Pure Appl. Math., 14, 415, 10.1002/cpa.3160140317 Jones, 1980, Extension theorems for BMO, Indiana Univ. Math. J., 29, 41, 10.1512/iumj.1980.29.29005 Ladyzhenskaya, 1968, Linear and Quasilinear Equations of Parabolic Type, Vol. 23 Ladyzhenskaya, 1968 Ladyzhenskaya, 1986, A survey of results on the solubility of boundary-value problems for second-order uniformly elliptic and parabolic quasi-linear equations having unbounded singularities, Russian Math. Surveys, 41, 1, 10.1070/RM1986v041n05ABEH003415 Markowich, 1986 Maugeri, 1998, Boundary value problem with an oblique derivative for uniformly elliptic operators with discontinuous coefficients, Forum Math., 10, 393, 10.1515/form.10.4.393 Maugeri, 2000 Merion, 1990 A.I. Nazarov, Hölder estimates for bounded solutions of problems with an oblique derivative for parabolic equations of nondivergence structure, J. Soviet Math. 64 (6) (1993) 1247–1252 (Transl. from Probl. Mat. Anal. (11) (1990) 37–46). A.I. Nazarov, N.N. Ural'tseva, Convex-monotone hulls and estimation of the maximum of a solution of a parabolic equation, J. Soviet Math. 37 (1987) 851–859 (Transl. from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. im. V.A. Steklov AN SSSR 147 (1985) 95–109). A.I. Nazarov, N.N. Ural'tseva, The oblique boundary-value problem for a quasilinear parabolic equation, J. Math. Sci. 77 (3) (1995) 3212–3220 (Transl. from Zap. Nauchn. Semin. POMI 200 (1992) 118–131). Palagachev, 1995, Quasilinear elliptic equations with VMO coefficients, Trans. Amer. Math. Soc., 347, 2481, 10.2307/2154833 Palagachev, 2000, Regular oblique derivative problem in Morrey spaces, Electron. J. Differential Equations, 2000, 1 Popivanov, 1997 Sarason, 1975, On functions of vanishing mean oscillation, Trans. Amer. Math. Soc., 207, 391, 10.1090/S0002-9947-1975-0377518-3 Softova, 2000, Oblique derivative problem for parabolic operators with VMO coefficients, Manuscripta Math., 103, 203, 10.1007/PL00022744 L.G. Softova, Parabolic equations with VMO coefficients in Morrey spaces, Electron J. Differential Equations 2001 (51) (2001) 1–25, http://ejde.math.swt.edu/Volumes/2001/51. Tomi, 1969, Über semilineare elliptische Differentialgleichungen zweiter Ordnung, Math. Z., 111, 350, 10.1007/BF01110746 Von Wahl, 1973, Über quasilineare differentialgleichungen in der Ebene, Manuscripta Math., 8, 59, 10.1007/BF01317577