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Solving strongly monotone variational and quasi-variational inequalities
Quasilinear divergence form parabolic equations in Reifenberg flat domains
1. | Department of Mathematics, Polytechnic University of Bari, 4 E. Orabona Str., 70 125 Bari |
2. | Dipartimento di Ingegneria Civile, Seconda Università di Napoli, Via Roma, 29; 81 031 Aversa, Italy |
References:
[1] |
A. A. Arkhipova, $L_p$-estimates of the gradients of solutions of initial/boundary-value problems for quasilinear parabolic systems. Differential and pseudodifferential operators, J. Math. Sci., 73 (1995), 609-617.
doi: 10.1007/BF02364939. |
[2] |
A. A. Arkhipova, Reverse Hölder inequalities with boundary integrals and $L_p$-estimates for solutions of nonlinear elliptic and parabolic boundary-value problems, in "Nonlinear Evolution Equations" (ed. N. N. Uraltseva), Amer. Math. Soc. Transl. Ser. 2, 164, Amer. Math. Soc., Providence, RI, (1995), 15-42. |
[3] |
S.-S. Byun and L. Wang, Parabolic equations in Reifenberg domains, Arch. Ration. Mech. Anal., 176 (2005), 271-301.
doi: 10.1007/s00205-005-0357-6. |
[4] |
S.-S. Byun and L. Wang, $L^p$ estimates for parabolic equations in Reifenberg domains, J. Funct. Anal., 223 (2005), 44-85.
doi: 10.1016/j.jfa.2004.10.014. |
[5] |
S.-S. Byun, Optimal $W^{1,p}$ regularity theory for parabolic equations in divergence form, J. Evol. Equ., 7 (2007), 415-428.
doi: 10.1007/s00028-007-0278-y. |
[6] |
S.-S. Byun and L. Wang, Parabolic equations in time dependent Reifenberg domains, Adv. Math., 212 (2007), 797-818.
doi: 10.1016/j.aim.2006.12.002. |
[7] |
O. A. Ladyžhenskaya, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Transl. Math. Monographs, Vol. 23, Amer. Math. Soc., Providence, R.I., 1967. |
[8] |
G. Lieberman, "Second Order Parabolic Differential Equations," World Scientific Publishing Co., Inc., River Edge, NJ, 1996. |
[9] |
A. Maugeri, D. K. Palagachev and L. G. Softova, "Elliptic and Parabolic Equations with Discontinuous Coefficients," Mathematical Research, 109, Wiley-VCH Verlag Berlin GmbH, Berlin, 2000. |
[10] |
J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., 80 (1958), 931-954.
doi: 10.2307/2372841. |
[11] |
D. K. Palagachev, Quasilinear elliptic equations with $VMO$ coefficients, Trans. Amer. Math. Soc., 347 (1995), 2481-2493.
doi: 10.2307/2154833. |
[12] |
D. K. Palagachev, L. Recke and L. G. Softova, Applications of the differential calculus to nonlinear elliptic operators with discontinuous coefficients, Math. Ann., 336 (2006), 617-637.
doi: 10.1007/s00208-006-0014-x. |
[13] |
E. R. Reifenberg, Solution of the Plateau problem for $m$-dimensional surfaces of varying topological type, Acta Math., 104 (1960), 1-92.
doi: 10.1007/BF02547186. |
[14] |
T. Toro, Doubling and flatness: Geometry of measures, Notices Amer. Math. Soc., 44 (1997), 1087-1094. |
show all references
References:
[1] |
A. A. Arkhipova, $L_p$-estimates of the gradients of solutions of initial/boundary-value problems for quasilinear parabolic systems. Differential and pseudodifferential operators, J. Math. Sci., 73 (1995), 609-617.
doi: 10.1007/BF02364939. |
[2] |
A. A. Arkhipova, Reverse Hölder inequalities with boundary integrals and $L_p$-estimates for solutions of nonlinear elliptic and parabolic boundary-value problems, in "Nonlinear Evolution Equations" (ed. N. N. Uraltseva), Amer. Math. Soc. Transl. Ser. 2, 164, Amer. Math. Soc., Providence, RI, (1995), 15-42. |
[3] |
S.-S. Byun and L. Wang, Parabolic equations in Reifenberg domains, Arch. Ration. Mech. Anal., 176 (2005), 271-301.
doi: 10.1007/s00205-005-0357-6. |
[4] |
S.-S. Byun and L. Wang, $L^p$ estimates for parabolic equations in Reifenberg domains, J. Funct. Anal., 223 (2005), 44-85.
doi: 10.1016/j.jfa.2004.10.014. |
[5] |
S.-S. Byun, Optimal $W^{1,p}$ regularity theory for parabolic equations in divergence form, J. Evol. Equ., 7 (2007), 415-428.
doi: 10.1007/s00028-007-0278-y. |
[6] |
S.-S. Byun and L. Wang, Parabolic equations in time dependent Reifenberg domains, Adv. Math., 212 (2007), 797-818.
doi: 10.1016/j.aim.2006.12.002. |
[7] |
O. A. Ladyžhenskaya, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Transl. Math. Monographs, Vol. 23, Amer. Math. Soc., Providence, R.I., 1967. |
[8] |
G. Lieberman, "Second Order Parabolic Differential Equations," World Scientific Publishing Co., Inc., River Edge, NJ, 1996. |
[9] |
A. Maugeri, D. K. Palagachev and L. G. Softova, "Elliptic and Parabolic Equations with Discontinuous Coefficients," Mathematical Research, 109, Wiley-VCH Verlag Berlin GmbH, Berlin, 2000. |
[10] |
J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., 80 (1958), 931-954.
doi: 10.2307/2372841. |
[11] |
D. K. Palagachev, Quasilinear elliptic equations with $VMO$ coefficients, Trans. Amer. Math. Soc., 347 (1995), 2481-2493.
doi: 10.2307/2154833. |
[12] |
D. K. Palagachev, L. Recke and L. G. Softova, Applications of the differential calculus to nonlinear elliptic operators with discontinuous coefficients, Math. Ann., 336 (2006), 617-637.
doi: 10.1007/s00208-006-0014-x. |
[13] |
E. R. Reifenberg, Solution of the Plateau problem for $m$-dimensional surfaces of varying topological type, Acta Math., 104 (1960), 1-92.
doi: 10.1007/BF02547186. |
[14] |
T. Toro, Doubling and flatness: Geometry of measures, Notices Amer. Math. Soc., 44 (1997), 1087-1094. |
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