Jesus Idelfonso Diaz, Jean-Michel Rakotoson
Abstract:
We revisit the regularity of very weak solution to second-order elliptic
equations Lu=f in
with u=0 on
for
,
the distance to the boundary
.
While doing this, we extend our previous results
(and many others in the literature) by allowing the presence of
distributions f+g which are more general than Radon measures
(more precisely with g in the dual of suitable Lorentz-Sobolev spaces)
and by making weaker assumptions on the coefficients of L.
One of the new tools is a Hardy type inequality developed
recently by the second author. Applications to the study of the gradient
of solutions of some singular semilinear equations are also given.
Published February 10, 2014.
Math Subject Classifications: 35J25, 35J60, 35P30, 35J67.
Key Words: Very weak solutions; semilinear elliptic equations;
distance to the boundary; weighted spaces measure;
Hardy inequalities; Hardy spaces.
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Jesús Idelfonso Díaz Instituto de Matemática Interdisciplinar and Departamento de Matemática Aplicada Universidad Complutense de Mmadrid Plaza de las Ciencias No. 3, 28040 Madrid, Spain email: diaz.racefyn@insde.es | |
Jean-Michel Rakotoson Laboratoire de Mathématiques et Applications Université de Poitiers Boulevard Marie et Pierre Curie, Teleport 2, BP 30179 86962 Futuroscope Chasseneuil Cedex, France email: rako@math.univ-poitiers.fr |
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