730 research outputs found
Some remarks on the duality method for Integro-Differential equations with measure data
We deal with existence, uniqueness, and regularity for solutions of the
boundary value problem
where
is a bounded domain of , is a bounded radon
measure on , and is a nonlocal operator of fractional
order whose kernel is comparable with the one of the factional
laplacian
Non-stationary Magnetic Microstructures in Stellar Thin Accretion Discs
We examine the morphology of magnetic structures in thin plasma accretion
discs, generalizing a stationary ideal MHD model to the time-dependent
visco-resistive case. Our analysis deals with small scale perturbations to a
central dipole-like magnetic field, which give rise -- as in the ideal case --
to the periodic modulation of magnetic flux surfaces along the radial
direction, corresponding to the formation of a toroidal current channels
sequence. These microstructures suffer an exponential damping in time because
of the non-zero resistivity coefficient, allowing us to define a configuration
lifetime which mainly depends on the midplane temperature and on the length
scale of the structure itself. By means of this lifetime we show that the
microstructures can exist within the inner region of stellar discs in a precise
range of temperatures, and that their duration is consistent with local
transient processes (minutes to hours).Comment: 14 text pages, 5 figures, to be published on PR
On singular elliptic equations with measure sources
We prove existence of solutions for a class of singular elliptic problems
with a general measure as source term whose model is
where
is an open bounded subset of . Here , is
a nonnegative function on , and is a nonnegative bounded Radon
measure on
A Lazer-McKenna type problem with measures
In this paper we are concerned with a general singular Dirichlet boundary
value problem whose model is the following Here is a nonnegative bounded Radon measure on a bounded
open set , and
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