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Abstract:

In this paper we study the H2 global regularity for solutions of the p(x)-Laplacian in two-dimensional convex domains with Dirichlet boundary conditions. Here p:Ω→[p1, ∞) with p∈Lip(Ω-) and p1>1. © 2013 Elsevier Inc.

Registro:

Documento: Artículo
Título:H2 regularity for the p(x)-Laplacian in two-dimensional convex domains
Autor:Del Pezzo, L.M.; Martínez, S.
Filiación:CONICET and Departamento de Matemática, FCEyN, UBA, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina
IMAS-CONICET and Departamento de Matemática, FCEyN, UBA, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Idioma: Inglés
Palabras clave:Elliptic equations; H2 regularity; Variable exponent spaces
Año:2014
Volumen:410
Número:2
Página de inicio:939
Página de fin:952
DOI: http://dx.doi.org/10.1016/j.jmaa.2013.09.016
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_0022247X_v410_n2_p939_DelPezzo

Referencias:

  • Acerbi, E., Mingione, G., Regularity results for a class of functionals with non-standard growth (2001) Arch. Ration. Mech. Anal., 156 (2), pp. 121-140
  • Baranger, J., Najib, K., Analyse numérique des écoulements quasi-newtoniens dont la viscosité obéit à la loi puissance ou la loi de carreau (1990) Numer. Math., 58 (1), pp. 35-49
  • Bollt, E.M., Chartrand, R., Esedoglu, S., Schultz, P., Vixie, K.R., Graduated adaptive image denoising: local compromise between total variation and isotropic diffusion (2009) Adv. Comput. Math., 31 (1-3), pp. 61-85
  • Challal, S., Lyaghfouri, A., Second order regularity for the p(x)-Laplace operator (2011) Math. Nachr., 284 (10), pp. 1270-1279
  • Chen, Y., Levine, S., Rao, M., Variable exponent, linear growth functionals in image restoration (2006) SIAM J. Appl. Math., 66 (4), pp. 1383-1406. , (electronic)
  • Ciarlet, P., (1978) The Finite Element Method for Elliptic Problems, vol. 68, , North-Holland, Amsterdam
  • Coscia, A., Mingione, G., Hölder continuity of the gradient of p(x) harmonic mappings (1999) C. R. Acad. Sci. Ser. I Math., 328, pp. 363-368
  • Del Pezzo, L.M., Lombardi, A.L., Martínez, S., Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian (2012) SIAM J. Numer. Anal., 50 (5), pp. 2497-2521
  • Diening, L., (2002) Theoretical and numerical results for electrorheological fluids, , PhD thesis, University of Freiburg, Germany
  • Diening, L., Maximal function on generalized Lebesgue spaces Lp({dot operator}) (2004) Math. Inequal. Appl., 7 (2), pp. 245-253
  • Diening, L., Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp({dot operator}) and Wk,p({dot operator}) (2004) Math. Nachr., 268, pp. 31-43
  • Diening, L., Harjulehto, P., Hästö, P., Ruzicka, M., Lebesgue and Sobolev Spaces with Variable Exponents (2011) Lecture Notes in Math., 2017. , Springer-Verlag, New York
  • Diening, L., Hästö, P., Nekvinda, A., Open problems in variable exponent Lebesgue and Sobolev spaces (2005) Function Spaces, Differential Operators and Nonlinear Analysis, , Math. Inst. Acad. Sci. Czech Republic, Praha
  • Edmunds, D.E., Rákosník Jiří, Sobolev embeddings with variable exponent (2000) Studia Math., 143 (3), pp. 267-293
  • Esposito, L., Leonetti, F., Mingione, G., Sharp regularity for functionals with (p, q) growth (2004) J. Differential Equations, 204 (1), pp. 5-55
  • Evans, L.C., Gariepy, R.F., Measure Theory and Fine Properties of Functions (1992) Stud. Adv. Math., , CRC Press, Boca Raton, FL
  • Fan, X., Global C1,α regularity for variable exponent elliptic equations in divergence form (2007) J. Differential Equations, 235 (2), pp. 397-417
  • Fan, X., Zhao, D., A class of De Giorgi type and Hölder continuity (1999) Nonlinear Anal., Ser. A: Theory Methods, 36 (3), pp. 295-318
  • Gilbarg, D., Trudinger, N.S., Elliptic Partial Differential Equations of Second Order (1983) Grundlehren Math. Wiss., 224. , Springer-Verlag, Berlin
  • Grisvard, P., Elliptic Problems in Nonsmooth Domains (1985) Monogr. Stud. Math., 24. , Pitman (Advanced Publishing Program), Boston, MA
  • Kováčik, O., Rákosník, J., On spaces Lp(x) and Wk,p(x) (1991) Czechoslovak Math. J., 41, pp. 592-618
  • Liu, W.B., Barrett, J.W., A remark on the regularity of the solutions of the p-Laplacian and its application to their finite element approximation (1993) J. Math. Anal. Appl., 178 (2), pp. 470-487
  • Miranda, C., Partial Differential Equations of Elliptic Type (1970) Ergeb. Math. Grenzgeb., 2. , Springer-Verlag, New York, translated from the Italian by Zane C. Motteler
  • Růžička, M., Electrorheological Fluids: Modeling and Mathematical Theory (2000) Lecture Notes in Math., 1748. , Springer-Verlag, Berlin
  • Samko, S., Denseness of C0∞(RN) in the generalized Sobolev spaces WM,P(X)(RN) (2000) Int. Soc. Anal. Appl. Comput., 5, pp. 333-342. , Kluwer Acad. Publ., Dordrecht, Direct and Inverse Problems of Mathematical Physics

Citas:

---------- APA ----------
Del Pezzo, L.M. & Martínez, S. (2014) . H2 regularity for the p(x)-Laplacian in two-dimensional convex domains. Journal of Mathematical Analysis and Applications, 410(2), 939-952.
http://dx.doi.org/10.1016/j.jmaa.2013.09.016
---------- CHICAGO ----------
Del Pezzo, L.M., Martínez, S. "H2 regularity for the p(x)-Laplacian in two-dimensional convex domains" . Journal of Mathematical Analysis and Applications 410, no. 2 (2014) : 939-952.
http://dx.doi.org/10.1016/j.jmaa.2013.09.016
---------- MLA ----------
Del Pezzo, L.M., Martínez, S. "H2 regularity for the p(x)-Laplacian in two-dimensional convex domains" . Journal of Mathematical Analysis and Applications, vol. 410, no. 2, 2014, pp. 939-952.
http://dx.doi.org/10.1016/j.jmaa.2013.09.016
---------- VANCOUVER ----------
Del Pezzo, L.M., Martínez, S. H2 regularity for the p(x)-Laplacian in two-dimensional convex domains. J. Math. Anal. Appl. 2014;410(2):939-952.
http://dx.doi.org/10.1016/j.jmaa.2013.09.016