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Título de Acceso Abierto

Regularidad Besov espacio temporal de temperaturas

Ivana Gómez Hugo Aimar Julián Fernández Bonder Francisco Javier Martín Reyes Gladis Pradolini Bibiana Iaffei

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Resumen/Descripción – provisto por el repositorio digital
This thesis aims to prove Besov regularity properties of temperatures. The results by David Jerison and Carlos Kenig for the elliptic case, suggest that, for solutions of the heat equation in cylindrical domains based on Lipschitz regions, some Besov regularity properties in the space variables could become, under diffusion, into joint space-time regularity. The main result contained in this thesis shows that this joint regularity in space and time is attained if the space regularity has some precise integrability properties in the time variable. The most technical aspects of this thesis are precisely those needed to get that integrality property. Moreover, the central tool is a pointwise estimate for the gradients of temperatures in terms of the iteration of two well known operators in harmonic analysis: the one sided Hardy-Littlewood maximal operator and the Calderón maximal function. To introduce a way to measure the joint regularity in space and time, we introduce through interpolation a family of Parabolic Besov spaces.
Palabras clave – provistas por el repositorio digital

Besov spaces; Heat equation; Mean value formula; Maximal operators; Gradient estimates; Espacios de besov; Ecuación del calor; Fórmulas del valor medio; Operadores maximales; Estimaciones de gradientes

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No requiere 2008 Biblioteca Virtual de la Universidad Nacional del Litoral (SNRD) acceso abierto

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Tipo de recurso:

tesis

Idiomas de la publicación

  • español castellano

País de edición

Argentina

Fecha de publicación