- Previous Article
- DCDS-B Home
- This Issue
-
Next Article
Higher integrability results for non smooth parabolic systems: The subquadratic case
Existence of bounded solutions to some nonlinear degenerate elliptic systems
1. | Università di L'Aquila, Dipartimento di Matematica Pura ed Applicata, Via Vetoio, Coppito, 67100 L'Aquila, Italy |
2. | Via Sant’Amasio 18, 03039 Sora, Italy |
-div $( a(x, u(x), Du(x) ) ) = f(x),$ $
x \in \Omega$;
$u(x) = 0, $ $
x \in \partial\Omega$
where $\Omega$ is a bounded open set, $a$ is a suitable degenerate elliptic operator and $f$ has enough integrability.
[1] |
Francisco Ortegón Gallego, María Teresa González Montesinos. Existence of a capacity solution to a coupled nonlinear parabolic--elliptic system. Communications on Pure and Applied Analysis, 2007, 6 (1) : 23-42. doi: 10.3934/cpaa.2007.6.23 |
[2] |
H. M. Yin. Optimal regularity of solution to a degenerate elliptic system arising in electromagnetic fields. Communications on Pure and Applied Analysis, 2002, 1 (1) : 127-134. doi: 10.3934/cpaa.2002.1.127 |
[3] |
Dominique Blanchard, Nicolas Bruyère, Olivier Guibé. Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2213-2227. doi: 10.3934/cpaa.2013.12.2213 |
[4] |
Adnan Ben Aziza, Mohamed Ben Chrouda. Characterization for the existence of bounded solutions to elliptic equations. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 1157-1170. doi: 10.3934/dcds.2019049 |
[5] |
Yuya Tanaka, Tomomi Yokota. Finite-time blow-up in a quasilinear degenerate parabolic–elliptic chemotaxis system with logistic source and nonlinear production. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022075 |
[6] |
N. V. Chemetov. Nonlinear hyperbolic-elliptic systems in the bounded domain. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1079-1096. doi: 10.3934/cpaa.2011.10.1079 |
[7] |
Annamaria Canino, Elisa De Giorgio, Berardino Sciunzi. Second order regularity for degenerate nonlinear elliptic equations. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 4231-4242. doi: 10.3934/dcds.2018184 |
[8] |
Hua Chen, Yawei Wei. Multiple solutions for nonlinear cone degenerate elliptic equations. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2505-2518. doi: 10.3934/cpaa.2020272 |
[9] |
Yuxia Guo, Jianjun Nie. Classification for positive solutions of degenerate elliptic system. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1457-1475. doi: 10.3934/dcds.2018130 |
[10] |
Feng Li, Yuxiang Li. Global existence of weak solution in a chemotaxis-fluid system with nonlinear diffusion and rotational flux. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5409-5436. doi: 10.3934/dcdsb.2019064 |
[11] |
Diane Denny. A unique positive solution to a system of semilinear elliptic equations. Conference Publications, 2013, 2013 (special) : 193-195. doi: 10.3934/proc.2013.2013.193 |
[12] |
Mónica Clapp, Jorge Faya. Multiple solutions to a weakly coupled purely critical elliptic system in bounded domains. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3265-3289. doi: 10.3934/dcds.2019135 |
[13] |
Inbo Sim, Yun-Ho Kim. Existence of solutions and positivity of the infimum eigenvalue for degenerate elliptic equations with variable exponents. Conference Publications, 2013, 2013 (special) : 695-707. doi: 10.3934/proc.2013.2013.695 |
[14] |
Pierpaolo Soravia. Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients. Communications on Pure and Applied Analysis, 2006, 5 (1) : 213-240. doi: 10.3934/cpaa.2006.5.213 |
[15] |
Martino Bardi, Paola Mannucci. On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations. Communications on Pure and Applied Analysis, 2006, 5 (4) : 709-731. doi: 10.3934/cpaa.2006.5.709 |
[16] |
Françoise Demengel, O. Goubet. Existence of boundary blow up solutions for singular or degenerate fully nonlinear equations. Communications on Pure and Applied Analysis, 2013, 12 (2) : 621-645. doi: 10.3934/cpaa.2013.12.621 |
[17] |
Dongho Chae. Existence of a semilinear elliptic system with exponential nonlinearities. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 709-718. doi: 10.3934/dcds.2007.18.709 |
[18] |
Jian Zhang, Wen Zhang, Xiaoliang Xie. Existence and concentration of semiclassical solutions for Hamiltonian elliptic system. Communications on Pure and Applied Analysis, 2016, 15 (2) : 599-622. doi: 10.3934/cpaa.2016.15.599 |
[19] |
Federica Mennuni, Addolorata Salvatore. Existence of minimizers for a quasilinear elliptic system of gradient type. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022013 |
[20] |
Shun Kodama. A concentration phenomenon of the least energy solution to non-autonomous elliptic problems with a totally degenerate potential. Communications on Pure and Applied Analysis, 2017, 16 (2) : 671-698. doi: 10.3934/cpaa.2017033 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]