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Abstract:

The improved Poincaré inequality ||φ-φΩ||Lp(Ω)≤C||d∇φ||Lp(Ω) Where Ω ⊂ Rn is a bounded domain and d(x) is the distance from x to the boundary of Ω, has many applications. In particular, it can be used to obtain a decomposition of functions with vanishing integral into a sum of locally supported functions with the same property. Consequently, it can be used to go from local to global results, i.e., to extend to very general bounded domains results which are known for cubes. For example, this methodology can be used to prove the existence of solutions of the divergence in Sobolev spaces. The goal of this paper is to analyze the generalization of these results to the case of weighted norms. When the weight is in Ap the arguments used in the un-weighted case can be extended without great difficulty. However, we will show that the improved Poincaré inequality, as well as its above mentioned applications, can be extended to a more general class of weights.

Registro:

Documento: Artículo
Título:Improved Poincaré inequalities and solutions of the divergence in weighted norms
Autor:Acosta, G.; Cejas, M.E.; Durán, R.G.
Filiación:Universidad de Buenos Aires and IMAS-UBA-CONICET, Facultad de Ciencias Exactas y Naturales, Departamento de Matemática Pabellón I, Ciudad Universitaria, Caba, 1428, Argentina
Universidad Nacional de La Plata, CONICET Facultad de Ciencias Exactas, Departamento de Matemática, Calle 50 y 115, La Plata, Buenos Aires, 1900, Argentina
Palabras clave:Divergence operator; Poincaré inequalities; Weights
Año:2017
Volumen:42
Número:1
Página de inicio:211
Página de fin:226
DOI: http://dx.doi.org/10.5186/aasfm.2017.4212
Título revista:Annales Academiae Scientiarum Fennicae Mathematica
Título revista abreviado:Ann. Acad. Sci. Fenn. Math.
ISSN:1239629X
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_1239629X_v42_n1_p211_Acosta

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Citas:

---------- APA ----------
Acosta, G., Cejas, M.E. & Durán, R.G. (2017) . Improved Poincaré inequalities and solutions of the divergence in weighted norms. Annales Academiae Scientiarum Fennicae Mathematica, 42(1), 211-226.
http://dx.doi.org/10.5186/aasfm.2017.4212
---------- CHICAGO ----------
Acosta, G., Cejas, M.E., Durán, R.G. "Improved Poincaré inequalities and solutions of the divergence in weighted norms" . Annales Academiae Scientiarum Fennicae Mathematica 42, no. 1 (2017) : 211-226.
http://dx.doi.org/10.5186/aasfm.2017.4212
---------- MLA ----------
Acosta, G., Cejas, M.E., Durán, R.G. "Improved Poincaré inequalities and solutions of the divergence in weighted norms" . Annales Academiae Scientiarum Fennicae Mathematica, vol. 42, no. 1, 2017, pp. 211-226.
http://dx.doi.org/10.5186/aasfm.2017.4212
---------- VANCOUVER ----------
Acosta, G., Cejas, M.E., Durán, R.G. Improved Poincaré inequalities and solutions of the divergence in weighted norms. Ann. Acad. Sci. Fenn. Math. 2017;42(1):211-226.
http://dx.doi.org/10.5186/aasfm.2017.4212