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Abstract:

We obtain a Harnack type inequality for solutions to elliptic equations in divergence form with non-standard p(x)-type growth. A model equation is the inhomogeneous p(x)-Laplacian. Namely, Δp(x)u := div(|∇u|p(x)-2∇u) = f(x) in Ω for which we prove Harnack's inequality when f ∈ Lq0 (Ω) if max {1, N/p1} < q0 ≤ ∞. The constant in Harnack's inequality depends on u only through |||u|p(x)||p2-p1L1(Ω). Dependence of the constant on u is known to be necessary in the case of variable p(x). As in previous papers, log-Hölder continuity on the exponent p(x) is assumed. We also prove that weak solutions are locally bounded and Hölder continuous when f ∈ Lq0(x)(Ω) with q0 ∈ c(Ω) and max{1,N/p(x)} < q0(x) in Ω. These results are then generalized to elliptic equations div A(x,u,∇u) = B(x,u,∇u) with p(x)-type growth.

Registro:

Documento: Artículo
Título:Local bounds, Harnack's inequality and Hölder continuity for divergence type elliptic equations with non-standard growth
Autor:Wolanski, N.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, and IMAS-CONICET, Buenos Aires, 1428, Argentina
Palabras clave:Harnack's inequality; Local bounds; Variable exponent spaces
Año:2015
Volumen:56
Número:1
Página de inicio:73
Página de fin:105
Título revista:Revista de la Union Matematica Argentina
Título revista abreviado:Rev. Union Mat. Argent.
ISSN:00416932
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n1_p73_Wolanski

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Citas:

---------- APA ----------
(2015) . Local bounds, Harnack's inequality and Hölder continuity for divergence type elliptic equations with non-standard growth. Revista de la Union Matematica Argentina, 56(1), 73-105.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n1_p73_Wolanski [ ]
---------- CHICAGO ----------
Wolanski, N. "Local bounds, Harnack's inequality and Hölder continuity for divergence type elliptic equations with non-standard growth" . Revista de la Union Matematica Argentina 56, no. 1 (2015) : 73-105.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n1_p73_Wolanski [ ]
---------- MLA ----------
Wolanski, N. "Local bounds, Harnack's inequality and Hölder continuity for divergence type elliptic equations with non-standard growth" . Revista de la Union Matematica Argentina, vol. 56, no. 1, 2015, pp. 73-105.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n1_p73_Wolanski [ ]
---------- VANCOUVER ----------
Wolanski, N. Local bounds, Harnack's inequality and Hölder continuity for divergence type elliptic equations with non-standard growth. Rev. Union Mat. Argent. 2015;56(1):73-105.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v56_n1_p73_Wolanski [ ]