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Regularity of the extremal solution for a biharmonic problem with general nonlinearity
1. | Laboratoire Amiénois de Mathématiques Fondamentale et Appliquée, Faculté de Mathématiques et d' Informatique, 33, rue Saint-Leu 80039 Amiens Cedex 1, France |
[1] |
Zongming Guo, Juncheng Wei. Liouville type results and regularity of the extremal solutions of biharmonic equation with negative exponents. Discrete and Continuous Dynamical Systems, 2014, 34 (6) : 2561-2580. doi: 10.3934/dcds.2014.34.2561 |
[2] |
Baishun Lai, Qing Luo. Regularity of the extremal solution for a fourth-order elliptic problem with singular nonlinearity. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 227-241. doi: 10.3934/dcds.2011.30.227 |
[3] |
Siamak RabieniaHaratbar. Inverse scattering and stability for the biharmonic operator. Inverse Problems and Imaging, 2021, 15 (2) : 271-283. doi: 10.3934/ipi.2020064 |
[4] |
Olivier Goubet. Regularity of extremal solutions of a Liouville system. Discrete and Continuous Dynamical Systems - S, 2019, 12 (2) : 339-345. doi: 10.3934/dcdss.2019023 |
[5] |
Juan Dávila, Louis Dupaigne, Marcelo Montenegro. The extremal solution of a boundary reaction problem. Communications on Pure and Applied Analysis, 2008, 7 (4) : 795-817. doi: 10.3934/cpaa.2008.7.795 |
[6] |
Teemu Tyni, Valery Serov. Scattering problems for perturbations of the multidimensional biharmonic operator. Inverse Problems and Imaging, 2018, 12 (1) : 205-227. doi: 10.3934/ipi.2018008 |
[7] |
Tran Ngoc Thach, Nguyen Huy Tuan, Donal O'Regan. Regularized solution for a biharmonic equation with discrete data. Evolution Equations and Control Theory, 2020, 9 (2) : 341-358. doi: 10.3934/eect.2020008 |
[8] |
Mostafa Fazly. Regularity of extremal solutions of nonlocal elliptic systems. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 107-131. doi: 10.3934/dcds.2020005 |
[9] |
Yuan Li. Extremal solution and Liouville theorem for anisotropic elliptic equations. Communications on Pure and Applied Analysis, 2021, 20 (12) : 4063-4082. doi: 10.3934/cpaa.2021144 |
[10] |
Filippo Gazzola. On the moments of solutions to linear parabolic equations involving the biharmonic operator. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3583-3597. doi: 10.3934/dcds.2013.33.3583 |
[11] |
Pasquale Candito, Giovanni Molica Bisci. Multiple solutions for a Navier boundary value problem involving the $p$--biharmonic operator. Discrete and Continuous Dynamical Systems - S, 2012, 5 (4) : 741-751. doi: 10.3934/dcdss.2012.5.741 |
[12] |
Teemu Tyni, Valery Serov. Inverse scattering problem for quasi-linear perturbation of the biharmonic operator on the line. Inverse Problems and Imaging, 2019, 13 (1) : 159-175. doi: 10.3934/ipi.2019009 |
[13] |
Markus Harju, Jaakko Kultima, Valery Serov, Teemu Tyni. Two-dimensional inverse scattering for quasi-linear biharmonic operator. Inverse Problems and Imaging, 2021, 15 (5) : 1015-1033. doi: 10.3934/ipi.2021026 |
[14] |
Jaakko Kultima, Valery Serov. Reconstruction of singularities in two-dimensional quasi-linear biharmonic operator. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022011 |
[15] |
Pascal Auscher, Sylvie Monniaux, Pierre Portal. The maximal regularity operator on tent spaces. Communications on Pure and Applied Analysis, 2012, 11 (6) : 2213-2219. doi: 10.3934/cpaa.2012.11.2213 |
[16] |
Chérif Amrouche, Yves Raudin. Singular boundary conditions and regularity for the biharmonic problem in the half-space. Communications on Pure and Applied Analysis, 2007, 6 (4) : 957-982. doi: 10.3934/cpaa.2007.6.957 |
[17] |
Angelo Favini, Rabah Labbas, Keddour Lemrabet, Stéphane Maingot, Hassan D. Sidibé. Resolution and optimal regularity for a biharmonic equation with impedance boundary conditions and some generalizations. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 4991-5014. doi: 10.3934/dcds.2013.33.4991 |
[18] |
Craig Cowan, Pierpaolo Esposito, Nassif Ghoussoub. Regularity of extremal solutions in fourth order nonlinear eigenvalue problems on general domains. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 1033-1050. doi: 10.3934/dcds.2010.28.1033 |
[19] |
Canghua Jiang, Kok Lay Teo, Ryan Loxton, Guang-Ren Duan. A neighboring extremal solution for an optimal switched impulsive control problem. Journal of Industrial and Management Optimization, 2012, 8 (3) : 591-609. doi: 10.3934/jimo.2012.8.591 |
[20] |
Jagmohan Tyagi, Ram Baran Verma. Positive solution to extremal Pucci's equations with singular and gradient nonlinearity. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 2637-2659. doi: 10.3934/dcds.2019110 |
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