# American Institute of Mathematical Sciences

November  2012, 32(11): 3819-3839. doi: 10.3934/dcds.2012.32.3819

## Coercivity of elliptic mixed boundary value problems in annulus of $\mathbb{R}^N$

 1 Departamento de Matemática Aplicada y Computación, Escuela Técnica Superior de Ingeniería - ICAI, Universidad Ponti cia Comillas, Alberto Aguilera, 25, 28015-Madrid, Spain

Received  July 2011 Revised  October 2011 Published  June 2012

In this paper is proved that the Strong Maximum Principle is satisfied for a wide class of linear elliptic boundary value problems of mixed type in an annulus of $\mathbb{R}^N$, $N\geq 1$, provided it is thin enough. The coercive character of these boundary value problems is obtained thanks to the characterization of the Strong Maximum Principle found in [3], proving that the principal eigenvalue associated to each boundary value problem may be as large as we wish, independently of the weight on the boundary, by taking the annulus thin enough.
Citation: Santiago Cano-Casanova. Coercivity of elliptic mixed boundary value problems in annulus of $\mathbb{R}^N$. Discrete & Continuous Dynamical Systems, 2012, 32 (11) : 3819-3839. doi: 10.3934/dcds.2012.32.3819
##### References:

show all references

##### References:
 [1] Tomas Godoy, Jean-Pierre Gossez, Sofia Paczka. On the principal eigenvalues of some elliptic problems with large drift. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 225-237. doi: 10.3934/dcds.2013.33.225 [2] Carlo Orrieri. A stochastic maximum principle with dissipativity conditions. Discrete & Continuous Dynamical Systems, 2015, 35 (11) : 5499-5519. doi: 10.3934/dcds.2015.35.5499 [3] Gabriele Bonanno, Giuseppina D'Aguì. Mixed elliptic problems involving the $p-$Laplacian with nonhomogeneous boundary conditions. Discrete & Continuous Dynamical Systems, 2017, 37 (11) : 5797-5817. doi: 10.3934/dcds.2017252 [4] Davide Guidetti. On hyperbolic mixed problems with dynamic and Wentzell boundary conditions. Discrete & Continuous Dynamical Systems - S, 2020, 13 (12) : 3461-3471. doi: 10.3934/dcdss.2020239 [5] Md. Haider Ali Biswas, Maria do Rosário de Pinho. A nonsmooth maximum principle for optimal control problems with state and mixed constraints - convex case. Conference Publications, 2011, 2011 (Special) : 174-183. doi: 10.3934/proc.2011.2011.174 [6] Fei-Ying Yang, Wan-Tong Li, Jian-Wen Sun. Principal eigenvalues for some nonlocal eigenvalue problems and applications. Discrete & Continuous Dynamical Systems, 2016, 36 (7) : 4027-4049. doi: 10.3934/dcds.2016.36.4027 [7] Alassane Niang. Boundary regularity for a degenerate elliptic equation with mixed boundary conditions. Communications on Pure & Applied Analysis, 2019, 18 (1) : 107-128. doi: 10.3934/cpaa.2019007 [8] Doyoon Kim, Seungjin Ryu. The weak maximum principle for second-order elliptic and parabolic conormal derivative problems. Communications on Pure & Applied Analysis, 2020, 19 (1) : 493-510. doi: 10.3934/cpaa.2020024 [9] Zhiyuan Wen, Meirong Zhang. On the optimization problems of the principal eigenvalues of measure differential equations with indefinite measures. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 3257-3274. doi: 10.3934/dcdsb.2020061 [10] Hugo Beirão da Veiga. A challenging open problem: The inviscid limit under slip-type boundary conditions.. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 231-236. doi: 10.3934/dcdss.2010.3.231 [11] José M. Arrieta, Simone M. Bruschi. Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a non uniformly Lipschitz deformation. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 327-351. doi: 10.3934/dcdsb.2010.14.327 [12] Lingju Kong, Roger Nichols. On principal eigenvalues of biharmonic systems. Communications on Pure & Applied Analysis, 2021, 20 (1) : 1-15. doi: 10.3934/cpaa.2020254 [13] J. R. L. Webb. Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 177-186. doi: 10.3934/dcdss.2008.1.177 [14] Chiun-Chuan Chen, Li-Chang Hung, Hsiao-Feng Liu. N-barrier maximum principle for degenerate elliptic systems and its application. Discrete & Continuous Dynamical Systems, 2018, 38 (2) : 791-821. doi: 10.3934/dcds.2018034 [15] Tomasz Komorowski, Adam Bobrowski. A quantitative Hopf-type maximum principle for subsolutions of elliptic PDEs. Discrete & Continuous Dynamical Systems - S, 2020, 13 (12) : 3495-3502. doi: 10.3934/dcdss.2020248 [16] Elvise Berchio, Filippo Gazzola, Dario Pierotti. Nodal solutions to critical growth elliptic problems under Steklov boundary conditions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 533-557. doi: 10.3934/cpaa.2009.8.533 [17] Théophile Chaumont-Frelet, Serge Nicaise, Jérôme Tomezyk. Uniform a priori estimates for elliptic problems with impedance boundary conditions. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2445-2471. doi: 10.3934/cpaa.2020107 [18] Vesselin Petkov. Location of eigenvalues for the wave equation with dissipative boundary conditions. Inverse Problems & Imaging, 2016, 10 (4) : 1111-1139. doi: 10.3934/ipi.2016034 [19] Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control & Related Fields, 2012, 2 (2) : 195-215. doi: 10.3934/mcrf.2012.2.195 [20] Giuseppina Guatteri, Federica Masiero. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Mathematical Control & Related Fields, 2021, 11 (4) : 829-855. doi: 10.3934/mcrf.2020048

2020 Impact Factor: 1.392