EXISTENCE OF ENTROPY SOLUTIONS FOR STRONGLY NONLINEAR ANISOTROPIC ELLIPTIC PROBLEM INVOLVING LOWER ORDER TERMS AND HARDY POTENTIAL
Year 2018,
Volume: 1 Issue: 2, 62 - 87, 31.07.2018
Elhoussine Azroul
,
Mohammed Bouziani
,
Hassane Hjiaj
Abstract
In this work, we give an existence result of entropy solutions for the following strongly nonlinear anisotropic elliptic Dirichlet problem.
References
- E. Azroul, A. Barbara, H. Hjiaj and M. B. Benboubker, Entropy solutions for nonhomognous anisotropic 4~p() problems, Applicaciones Mathematicae, 41, 2-3, 149-163 (2014).
- B. Abdellaoui, I. Peral and A. Primo, Elliptic problems with a Hardy potential and critical growth in the gradient, journal of Dierential Equations 239, 386-416 (2007).
- Y. Akdim, A. Salmani, Existence and uniqueness Results for nonlinear Anisotropic elliptic Equations, Journal of Nonlinear Evolution Equations and Applications(JNEEA)., 6 , 95-111 (2016).
- S. Antontsev and M.Chipot, Anisotropic equations: uniqueness and existence results, J. Dierential and Integral Equations 21(5-6), , 401-419 (2008).
- S. N. Antontsev and J. F. Rodrigues, On stationary thermorheological viscous ows, Ann. Univ.Ferrara Sez. VII Sci. Mat. 52, 19-36 (2007).
- M. Bendahmane, M. Chrif and S. El Manouni, An Approximation Result in Generalized Anisotripic Sobolev Spaces and Application, J. Anal. Appl., 30, 341-353 (2011).
- M. Chrif - S. El Manouni, On a strongly anisotropic equation with L1 data, Appl. Anal. 87(7), 865-871 (2008).
- A. Benkirane - M. Chrif - S. El Manouni, Existence results for strongly nonlinear elliptic equations of innite order, Z. Anal. Anwend. (J. Anal. Appl.) 26, 303-312 (2007).
- P. Benilan, L. Boccardo, T. Gallouet, R. Gariepy, M. Pierre and J. L . Vazquez, An L1- theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4, 241-273 (1995)
- L. Boccardo, T. Gallouet and P. Marcellini, Anisotropic equations in L1. Dierential Integral Equations 9, no. 1, 209-212 (1996).
- L. Boccardo, F. Murat, J.P. Puel, Existence of bounded solutions for non linear elliptic unilateral problems, Ann. Mat. Pura Appl. (4)152, 183-196 (1988).
- A. Cianchi, Symmetrization in anisotropic elliptic problems. Comm. Partial Differential Equations 32 , no. 4-6, 693-717 (2007).
- Andrea Cianchi, A Fully anisotropic Sobolev inequality, Pacic Journal of Mathematic, Vol. 196, No.2, 283-294 (2000).
- F. C^rstea and J. Vetois, Fundamental solutions for anisotropic elliptic equations: existence and a priori estimates. Comm. Partial Dierential Equations 40, no. 4, 727-765 (2015).
- Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth functionals in image processing, SIAM J. Appl. Math., 66, 1383-1406 (2006)
- R. Di Nardo and F. Feo, Existence and uniqueness for nonlinear anisotropic elliptic equations. Arch. Math. (Basel) 102, no. 2, 141-153 (2014).
- R. Di Nardo, F. Feo and O. Guibe, Uniqueness result for nonlinear anisotropic elliptic equations. Adv. Dierential Equations 18, no. 5-6, 433-458 (2013).
- L. Diening, P. Harjulehto, P. Hasto and M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents, Lecture Notes in Mathematics, vol. 2017, Springer-Verlag, Heidelberg, 2011.
- R. J. DiPerna and P. L. Lions, On the cauchy problem for Boltzmann equations : global existence and weak stability, Ann of Math, 130 (1) , 321-366 (1989).
Year 2018,
Volume: 1 Issue: 2, 62 - 87, 31.07.2018
Elhoussine Azroul
,
Mohammed Bouziani
,
Hassane Hjiaj
References
- E. Azroul, A. Barbara, H. Hjiaj and M. B. Benboubker, Entropy solutions for nonhomognous anisotropic 4~p() problems, Applicaciones Mathematicae, 41, 2-3, 149-163 (2014).
- B. Abdellaoui, I. Peral and A. Primo, Elliptic problems with a Hardy potential and critical growth in the gradient, journal of Dierential Equations 239, 386-416 (2007).
- Y. Akdim, A. Salmani, Existence and uniqueness Results for nonlinear Anisotropic elliptic Equations, Journal of Nonlinear Evolution Equations and Applications(JNEEA)., 6 , 95-111 (2016).
- S. Antontsev and M.Chipot, Anisotropic equations: uniqueness and existence results, J. Dierential and Integral Equations 21(5-6), , 401-419 (2008).
- S. N. Antontsev and J. F. Rodrigues, On stationary thermorheological viscous ows, Ann. Univ.Ferrara Sez. VII Sci. Mat. 52, 19-36 (2007).
- M. Bendahmane, M. Chrif and S. El Manouni, An Approximation Result in Generalized Anisotripic Sobolev Spaces and Application, J. Anal. Appl., 30, 341-353 (2011).
- M. Chrif - S. El Manouni, On a strongly anisotropic equation with L1 data, Appl. Anal. 87(7), 865-871 (2008).
- A. Benkirane - M. Chrif - S. El Manouni, Existence results for strongly nonlinear elliptic equations of innite order, Z. Anal. Anwend. (J. Anal. Appl.) 26, 303-312 (2007).
- P. Benilan, L. Boccardo, T. Gallouet, R. Gariepy, M. Pierre and J. L . Vazquez, An L1- theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4, 241-273 (1995)
- L. Boccardo, T. Gallouet and P. Marcellini, Anisotropic equations in L1. Dierential Integral Equations 9, no. 1, 209-212 (1996).
- L. Boccardo, F. Murat, J.P. Puel, Existence of bounded solutions for non linear elliptic unilateral problems, Ann. Mat. Pura Appl. (4)152, 183-196 (1988).
- A. Cianchi, Symmetrization in anisotropic elliptic problems. Comm. Partial Differential Equations 32 , no. 4-6, 693-717 (2007).
- Andrea Cianchi, A Fully anisotropic Sobolev inequality, Pacic Journal of Mathematic, Vol. 196, No.2, 283-294 (2000).
- F. C^rstea and J. Vetois, Fundamental solutions for anisotropic elliptic equations: existence and a priori estimates. Comm. Partial Dierential Equations 40, no. 4, 727-765 (2015).
- Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth functionals in image processing, SIAM J. Appl. Math., 66, 1383-1406 (2006)
- R. Di Nardo and F. Feo, Existence and uniqueness for nonlinear anisotropic elliptic equations. Arch. Math. (Basel) 102, no. 2, 141-153 (2014).
- R. Di Nardo, F. Feo and O. Guibe, Uniqueness result for nonlinear anisotropic elliptic equations. Adv. Dierential Equations 18, no. 5-6, 433-458 (2013).
- L. Diening, P. Harjulehto, P. Hasto and M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents, Lecture Notes in Mathematics, vol. 2017, Springer-Verlag, Heidelberg, 2011.
- R. J. DiPerna and P. L. Lions, On the cauchy problem for Boltzmann equations : global existence and weak stability, Ann of Math, 130 (1) , 321-366 (1989).