Anisotropic problem with non-local boundary conditions and measure data

• Autores: A. Kaboré, Stanislas Ouaro
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 23, Nº. 1, 2021, págs. 21-62
• Idioma: inglés
• DOI: 10.4067/S0719-06462021000100021
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Estudiamos un problema elíptico nolineal anisotrópico con condiciones de borde no-locales y data de medida. Probamos un resultado de existencia y unicidad de la solución de entropía.

  • English

    Abstract We study a nonlinear anisotropic elliptic problem with non-local boundary conditions and measure data. We prove an existence and uniqueness result of entropy solution.

• Referencias bibliográficas
  • Baalal, A.,Berghout, M.. (2019). The Dirichlet problems for nonlinear elliptic equations with variable exponent. Journal of Applied Analysis...
  • Benboubker, M. B.,Hjiaj, H.,Ouaro, S.. (2014). Entropy solutions to nonlinear elliptic anisotropic problem with variable exponent. Journal...
  • Bendahmane, M.,Karlsen, K. H.. (2006). Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres....
  • Bénilan, Ph.,Brézis, H.,Crandall, M. G.. (1975). A semilinear equation in L1(RN). Ann. Scuola. Norm. Sup. Pisa. 2. 523
  • Bénilan, Ph.,Boccardo, L.,Gallouët, T.,Gariepy, R.,Pierre, M.,Vazquez, J. L.. (1995). An L1 theory of existence and uniqueness of nonlinear...
  • Bonzi, B. K.,Ouaro, S.,Zongo, F. D. Y.. (2013). Entropy solution for nonlinear elliptic anisotropic homogeneous Neumann Problem. Int. J. Differ....
  • Boureanu, M. M.,Radulescu, V. D.. (2012). Anisotropic Neumann problems in Sobolev spaces with variable exponent. Nonlinear Anal. TMA. 75....
  • Koné, B.,Ouaro, S.,Zongo, F. D. Y.. (2013). Nonlinear elliptic anisotropic problem with Fourier boundary condition. Int. J. Evol. Equ. 8....
  • Chen, Y.,Levine, S.,Rao, M.. (2006). Variable exponent, linear growth functionals in image restoration. SIAM J. Appl. Math. 66. 1383
  • Diening, L.. (2002). Theoretical and Numerical Results for Electrorheological Fluids. University of Frieburg. Germany.
  • Diening, L.. (2004). Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp(.) and W1,p(.). Math. Nachr. 268....
  • Ding, Y.,Ha-Duong, T.,Giroire, J.,Mouma, V.. (2004). Modeling of single-phase ow for horizontal wells in a stratified medium. Computers and...
  • Fan, X.,Zhao, D.. (2001). On the spaces Lp(.)(Ω) and Wm,p(.)(Ω). J. Math. Anal. Appl.. 263. 424
  • Fan, X.. (2010). Anisotropic variable exponent Sobolev spaces and ⃗p(.) -Laplacian equations. Complex variables and Elliptic Equations. 55....
  • Giroire, J.,Ha-Duong, T.,Moumas, V.. (2005). A non-linear and non-local boundary condition for a diffusion equation in petroleum engineering....
  • Halmos, P.. (1950). Measure Theory. D. Van Nostrand Company. New York.
  • Halsey, T. C.. (1992). Electrorheological fluids. Science. 258. 761
  • Hudzik, H.. (1976). On generalized Orlicz-Sobolev space. Funct. Approximatio Comment. Math.. 4. 37-51
  • Ibrango, I.,Ouaro, S.. (2015). Entropy solutions for nonlinear Dirichlet problems. Annals of the university of craiova, Mathematics and Computer...
  • Ibrango, I.,Ouaro, S.. (2016). Entropy solutions for nonlinear elliptic anisotropic problems with homogeneous Neumann boundary condition....
  • Kaboré, A.,Ouaro, S.. (2020). Nonlinear Elliptic anisotropic problem involving non local boundary conditions with variable exponent and graph...
  • Konaté, I.,Ouaro, S.. (2016). Good Radon measure for anisotropic problems with variable exponent. Electron. J. Diff. Equ.. 2016. 1-19
  • Kovacik, O.,Rakosnik, J.. (1991). On spaces Lp(x) and W1.p(x). Czech. Math. J.. 41. 592-618
  • Kozhevnikova, L. M.. (2019). On solutions of elliptic equations with variable exponents and measure data in Rn. 1912:12432.
  • Kozhevnikova, L. M.. (2020). On solutions of anisotropic elliptic equations with variable exponent and measure data. Complex variables and...
  • Mihailescu, M.,Radulescu, V.. (2006). A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological...
  • Mihailescu, M.,Radulescu, V.. (2007). On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent. Proc. Amer....
  • Mihailescu, M.,Pucci, P.,Radulescu, V.. (2008). Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent....
  • Musielak, J.. (1983). Orlicz Spaces, and modular spaces. Springer. Berlin.
  • Nakano, H.. (1950). Modulared semi-ordered linear spaces. Maruzen Co. Ltd. Tokyo.
  • Nyanquini, I.,Ouaro, S.,Safimba, S.. (2013). Entropy solution to nonlinear multivalued elliptic problem with variable exponents and measure...
  • Orlicz, W.. (1931). Über konjugierte Exponentenfolgen. Studia Math.. 3. 200
  • Pfeifer, C.,Mavroidis, C.,Bar-Cohen, Y.,Dolgin, B.. (1999). Electrorheological fluid based force feedback device. 3840. Proc. 1999 SPIE Telemanipulator...
  • Radulescu, V.. (2015). Nonlinear elliptic equations with variable exponent: old and new. Nonlinear Anal.. 121. 336
  • Rajagopal, K. R.,Ruzicka, M.. (2001). Mathematical modelling of electrorheological fluids. Continuum Mech. Thermodyn.. 13. 59-78
  • Ruzicka, M.. (2000). Electrorheological fluids: modelling and mathematical theory. Springer-Verlag. Berlin.
  • Sanchon, M.,Urbano, J. M.. (2009). Entropy solutions for the p(x)-Laplace Equation. Trans. Amer. Math. Soc.. 361. 6387
  • Sert, U.,Soltanov, K.. (2019). On the solvability of a class of nonlinear elliptic type equation with variable exponen. Journal of Applied...
  • Troisi, M.. (1969). Teoremi di inclusione per spazi di Sobolev non isotropi. Ric. Mat.. 18. 3-24
  • Sharapudinov, I.. (1978). On the topology of the space Lp(t)([0; 1]). Math. Zametki. 26. 613
  • Showalter, R. E.. (1997). Mathematical Surveys and Monographs. American Mathematical Society. Providence, RI.
  • Tsenov, I.V.. (1961). Generalization of the problem of best approximation of a function in the space Ls. Uch. Zap. Dagestan Gos. Univ.. 7....
  • Winslow, W. M.. (1949). Induced Fibration of Suspensions. J. Applied Physics. 20. 1137