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Local well-posedness for a nonlinear dirac equation in spaces of almost critical dimension
$W^{1,p}$ regularity for the conormal derivative problem with parabolic BMO nonlinearity in reifenberg domains
1. | Department of Mathematical Sciences, Seoul National University, Seoul 151-747 |
2. | Department of Mathematics, University of Iowa, Iowa City, IA 52242 |
[1] |
Hongjie Dong, Xinghong Pan. On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4567-4592. doi: 10.3934/dcds.2021049 |
[2] |
Dian Palagachev, Lubomira G. Softova. Quasilinear divergence form parabolic equations in Reifenberg flat domains. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1397-1410. doi: 10.3934/dcds.2011.31.1397 |
[3] |
Zhang Chao, Minghua Yang. BMO type space associated with Neumann operator and application to a class of parabolic equations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1629-1645. doi: 10.3934/dcdsb.2021104 |
[4] |
Doyoon Kim, Seungjin Ryu. The weak maximum principle for second-order elliptic and parabolic conormal derivative problems. Communications on Pure and Applied Analysis, 2020, 19 (1) : 493-510. doi: 10.3934/cpaa.2020024 |
[5] |
G. Acosta, Julián Fernández Bonder, P. Groisman, J.D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions. Discrete and Continuous Dynamical Systems - B, 2002, 2 (2) : 279-294. doi: 10.3934/dcdsb.2002.2.279 |
[6] |
G. P. Trachanas, Nikolaos B. Zographopoulos. A strongly singular parabolic problem on an unbounded domain. Communications on Pure and Applied Analysis, 2014, 13 (2) : 789-809. doi: 10.3934/cpaa.2014.13.789 |
[7] |
Vo Van Au, Hossein Jafari, Zakia Hammouch, Nguyen Huy Tuan. On a final value problem for a nonlinear fractional pseudo-parabolic equation. Electronic Research Archive, 2021, 29 (1) : 1709-1734. doi: 10.3934/era.2020088 |
[8] |
Doyoon Kim, Hongjie Dong, Hong Zhang. Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4895-4914. doi: 10.3934/dcds.2016011 |
[9] |
H. Gajewski, I. V. Skrypnik. To the uniqueness problem for nonlinear parabolic equations. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 315-336. doi: 10.3934/dcds.2004.10.315 |
[10] |
Sun-Sig Byun, Yumi Cho. Lorentz-Morrey regularity for nonlinear elliptic problems with irregular obstacles over Reifenberg flat domains. Discrete and Continuous Dynamical Systems, 2015, 35 (10) : 4791-4804. doi: 10.3934/dcds.2015.35.4791 |
[11] |
Changchun Liu, Zhao Wang. Time periodic solutions for a sixth order nonlinear parabolic equation in two space dimensions. Communications on Pure and Applied Analysis, 2014, 13 (3) : 1087-1104. doi: 10.3934/cpaa.2014.13.1087 |
[12] |
T. A. Shaposhnikova, M. N. Zubova. Homogenization problem for a parabolic variational inequality with constraints on subsets situated on the boundary of the domain. Networks and Heterogeneous Media, 2008, 3 (3) : 675-689. doi: 10.3934/nhm.2008.3.675 |
[13] |
R.G. Duran, J.I. Etcheverry, J.D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 497-506. doi: 10.3934/dcds.1998.4.497 |
[14] |
Victor A. Galaktionov, Juan-Luis Vázquez. The problem Of blow-up in nonlinear parabolic equations. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 399-433. doi: 10.3934/dcds.2002.8.399 |
[15] |
Fabio Punzo. Support properties of solutions to nonlinear parabolic equations with variable density in the hyperbolic space. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 657-670. doi: 10.3934/dcdss.2012.5.657 |
[16] |
Vahagn Nersesyan. Approximate controllability of nonlinear parabolic PDEs in arbitrary space dimension. Mathematical Control and Related Fields, 2021, 11 (2) : 237-251. doi: 10.3934/mcrf.2020035 |
[17] |
Chi-Cheung Poon. Blowup rate of solutions of a degenerate nonlinear parabolic equation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5317-5336. doi: 10.3934/dcdsb.2019060 |
[18] |
Laurence Cherfils, Stefania Gatti, Alain Miranville. A doubly nonlinear parabolic equation with a singular potential. Discrete and Continuous Dynamical Systems - S, 2011, 4 (1) : 51-66. doi: 10.3934/dcdss.2011.4.51 |
[19] |
Changchun Liu. A fourth order nonlinear degenerate parabolic equation. Communications on Pure and Applied Analysis, 2008, 7 (3) : 617-630. doi: 10.3934/cpaa.2008.7.617 |
[20] |
Jeremy LeCrone, Gieri Simonett. On quasilinear parabolic equations and continuous maximal regularity. Evolution Equations and Control Theory, 2020, 9 (1) : 61-86. doi: 10.3934/eect.2020017 |
2020 Impact Factor: 1.392
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