8,578 research outputs found
Symmetrization for Linear and Nonlinear Fractional Parabolic Equations of Porous Medium Type
We establish symmetrization results for the solutions of the linear
fractional diffusion equation and
itselliptic counterpart , , using the
concept of comparison of concentrations. The results extend to the nonlinear
version, , but only when
A:\re_+\to\re_+ is a concave function. In the elliptic case, complete
symmetrization results are proved for \ when
is a convex nonnegative function for with , and partial
results when is concave. Remarkable counterexamples are constructed for the
parabolic equation when is convex, resp. for the elliptic equation when
is concave. Such counterexamples do not exist in the standard diffusion case
.Comment: 42 pages, 1 figur
Registros recientes delgasterópodo exótico Rapana venosa (Valenciennes, 1846) a lo largode la lÃnea costera Argentina: ¿Está progresandolainvasiónhaciaelsur?
Se presentan los registros más recientes de R. venosa a lo largo de la lÃnea costera de Argentina (2010-2013), incluyendo el hallazgo de un individuo en la albufera Mar Chiquita (200 km al sur del RÃo de la Plata). Se discuten los posibles mecanismos de expansión.Recent range extensions of R. venosa along the Argentine coastline are presented (2010-2013),including the finding of an individual in Mar Chiquita lagoon (200 km southwards of the RÃo de la Plata).We discuss potential mechanisms for this expansion.Fil: Giberto, Diego Agustin. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Subsede Instituto Nacional de Investigación y Desarrollo Pesquero; ArgentinaFil: Bruno, Luis Ignacio. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales; Argentin
Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application
We develop further the theory of symmetrization of fractional Laplacian
operators contained in recent works of two of the authors. The theory leads to
optimal estimates in the form of concentration comparison inequalities for both
elliptic and parabolic equations. In this paper we extend the theory for the
so-called \emph{restricted} fractional Laplacian defined on a bounded domain
of with zero Dirichlet conditions outside of .
As an application, we derive an original proof of the corresponding fractional
Faber-Krahn inequality. We also provide a more classical variational proof of
the inequality.Comment: arXiv admin note: substantial text overlap with arXiv:1303.297
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