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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.



Keywords

Anisotropic Sobolev spaces Strongly nonlinear elliptic equation Hardy potential Entropy solutions Lower order terms

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

Abstract

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).
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Elhoussine Azroul

Mohammed Bouziani

Hassane Hjiaj

Publication Date July 31, 2018
Submission Date May 17, 2018
Acceptance Date August 5, 2018
Published in Issue Year 2018 Volume: 1 Issue: 2

Cite

APA Azroul, E., Bouziani, M., & Hjiaj, H. (2018). EXISTENCE OF ENTROPY SOLUTIONS FOR STRONGLY NONLINEAR ANISOTROPIC ELLIPTIC PROBLEM INVOLVING LOWER ORDER TERMS AND HARDY POTENTIAL. Journal of Universal Mathematics, 1(2), 62-87.
AMA Azroul E, Bouziani M, Hjiaj H. EXISTENCE OF ENTROPY SOLUTIONS FOR STRONGLY NONLINEAR ANISOTROPIC ELLIPTIC PROBLEM INVOLVING LOWER ORDER TERMS AND HARDY POTENTIAL. JUM. July 2018;1(2):62-87.
Chicago Azroul, Elhoussine, Mohammed Bouziani, and Hassane Hjiaj. “EXISTENCE OF ENTROPY SOLUTIONS FOR STRONGLY NONLINEAR ANISOTROPIC ELLIPTIC PROBLEM INVOLVING LOWER ORDER TERMS AND HARDY POTENTIAL”. Journal of Universal Mathematics 1, no. 2 (July 2018): 62-87.
EndNote Azroul E, Bouziani M, Hjiaj H (July 1, 2018) EXISTENCE OF ENTROPY SOLUTIONS FOR STRONGLY NONLINEAR ANISOTROPIC ELLIPTIC PROBLEM INVOLVING LOWER ORDER TERMS AND HARDY POTENTIAL. Journal of Universal Mathematics 1 2 62–87.
IEEE E. Azroul, M. Bouziani, and H. Hjiaj, “EXISTENCE OF ENTROPY SOLUTIONS FOR STRONGLY NONLINEAR ANISOTROPIC ELLIPTIC PROBLEM INVOLVING LOWER ORDER TERMS AND HARDY POTENTIAL”, JUM, vol. 1, no. 2, pp. 62–87, 2018.
ISNAD Azroul, Elhoussine et al. “EXISTENCE OF ENTROPY SOLUTIONS FOR STRONGLY NONLINEAR ANISOTROPIC ELLIPTIC PROBLEM INVOLVING LOWER ORDER TERMS AND HARDY POTENTIAL”. Journal of Universal Mathematics 1/2 (July 2018), 62-87.
JAMA Azroul E, Bouziani M, Hjiaj H. EXISTENCE OF ENTROPY SOLUTIONS FOR STRONGLY NONLINEAR ANISOTROPIC ELLIPTIC PROBLEM INVOLVING LOWER ORDER TERMS AND HARDY POTENTIAL. JUM. 2018;1:62–87.
MLA Azroul, Elhoussine et al. “EXISTENCE OF ENTROPY SOLUTIONS FOR STRONGLY NONLINEAR ANISOTROPIC ELLIPTIC PROBLEM INVOLVING LOWER ORDER TERMS AND HARDY POTENTIAL”. Journal of Universal Mathematics, vol. 1, no. 2, 2018, pp. 62-87.
Vancouver Azroul E, Bouziani M, Hjiaj H. EXISTENCE OF ENTROPY SOLUTIONS FOR STRONGLY NONLINEAR ANISOTROPIC ELLIPTIC PROBLEM INVOLVING LOWER ORDER TERMS AND HARDY POTENTIAL. JUM. 2018;1(2):62-87.
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