Navegar

Colección

Datos Estadísticas

Artículo

La versión final de este artículo es de uso interno de la institución.
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

Let u be a weak solution of (-Δ)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ Rn. Then, the main goal of this paper is to prove the following a priori estimate: {double pipe}u{double pipe}Wω 2m,p(Ω) ≤ C{double pipe}f{double pipe}Lω p(Ω), where ω is a weight in the Muckenhoupt class Ap. © 2010 Editorial Board of Analysis in Theory and Applications and Springer-Verlag Berlin Heidelberg.

Registro:

Documento: Artículo
Título:Weighted a priori estimates for solution of (-Δ)mu = f with homogeneous dirichlet conditions
Autor:Durán, R.G.; Sanmartino, M.; Toschi, M.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Marcela Sanmartino and Marisa Toschi, Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Buenos Aires), Argentina
Palabras clave:Calderón-Zygmund theory; Dirichlet problem; Green function; weighted Sobolev space
Año:2010
Volumen:26
Número:4
Página de inicio:339
Página de fin:349
DOI: http://dx.doi.org/10.1007/s10496-010-0339-x
Título revista:Analysis in Theory and Applications
Título revista abreviado:Anal. Theory Appl.
ISSN:16724070
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16724070_v26_n4_p339_Duran

Referencias:

  • Agmon, S., Douglis, A., Nirenberg, L., Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions, I (1959) Comm. Pure Appl. Math., 12, pp. 623-727
  • Agmon, S., (1965) Lectures on Elliptic Boundary Value Problems, , Princeton, N.J.-Toronto-London: D. Van Nostrand Co., Inc., Prepared for Publication by B. Frank Jones, Jr. With the Assistance of George W. Batten, Jr. Van Nostrand Mathematical Studies, No. 2
  • Chua, S.-K., Extension Theorems on Weighted Sobolev spaces (1992) Indiana Univ. Math. J., 41 (4), pp. 1027-1076
  • Dall'Acqua, A., Sweers, G., Estimates for Green Function and Poisson Kernels of Higher-order Dirichlet Boundary Value Problems (2004) J. Differential Equations, 205 (2), pp. 466-487
  • Durán, R.G., Sanmartino, M., Toschi, M., (2008) Weighted a Priori Estimates for Poisson Equation, to Appear in Indiana University Math. J., 57 (7), pp. 3463-3478
  • Krasovskiǐ, J.P., Isolation of the Singularity in Green's Function (1967) Izv. Akad. Nauk SSSR Ser.Mat., 31, pp. 977-1010
  • Muckenhoupt, B., Weighted Norm Inequalities for the Hardy Maximal Function (1972) Trans. Amer. Math. Soc., 165, pp. 207-226
  • Stein, E.M., (1993) Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, 43. , Princeton Mathematical Series, Princeton, NJ: Princeton University Press

Citas:

---------- APA ----------
Durán, R.G., Sanmartino, M. & Toschi, M. (2010) . Weighted a priori estimates for solution of (-Δ)mu = f with homogeneous dirichlet conditions. Analysis in Theory and Applications, 26(4), 339-349.
http://dx.doi.org/10.1007/s10496-010-0339-x
---------- CHICAGO ----------
Durán, R.G., Sanmartino, M., Toschi, M. "Weighted a priori estimates for solution of (-Δ)mu = f with homogeneous dirichlet conditions" . Analysis in Theory and Applications 26, no. 4 (2010) : 339-349.
http://dx.doi.org/10.1007/s10496-010-0339-x
---------- MLA ----------
Durán, R.G., Sanmartino, M., Toschi, M. "Weighted a priori estimates for solution of (-Δ)mu = f with homogeneous dirichlet conditions" . Analysis in Theory and Applications, vol. 26, no. 4, 2010, pp. 339-349.
http://dx.doi.org/10.1007/s10496-010-0339-x
---------- VANCOUVER ----------
Durán, R.G., Sanmartino, M., Toschi, M. Weighted a priori estimates for solution of (-Δ)mu = f with homogeneous dirichlet conditions. Anal. Theory Appl. 2010;26(4):339-349.
http://dx.doi.org/10.1007/s10496-010-0339-x