121 research outputs found
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
Flat solutions of the 1-Laplacian equation
For every defined in an open bounded subset of
, we prove that a solution of the
-Laplacian equation in
satisfies on a set of positive Lebesgue measure. The
same property holds if has small norm in the
Marcinkiewicz space of weak- functions or if is a BV minimizer of
the associated energy functional. The proofs rely on Stampacchia's truncation
method.Comment: Dedicated to Jean Mawhin. Revised and extended version of a note
written by the authors in 201
Strong maximum principle for Schr\"odinger operators with singular potential
We prove that for every and for every potential , any
nonnegative function satisfying in an open connected
set of is either identically zero or its level set
has zero capacity. This gives an affirmative answer to an open
problem of B\'enilan and Brezis concerning a bridge between
Serrin-Stampacchia's strong maximum principle for and
Ancona's strong maximum principle for . The proof is based on the
construction of suitable test functions depending on the level set
and on the existence of solutions of the Dirichlet problem for the
Schr\"odinger operator with diffuse measure data.Comment: 21 page
A semilinear problem with a W^{1,1}_0 solution
We study a degenerate elliptic equation, proving the existence of a W^{1,1}_0
distributional solution
Existence of solutions for degenerate parabolic equations with singular terms
In this paper we deal with parabolic problems whose simplest model is
where , , , , and is a positive function in
bounded away from zero
The role of interplay between coefficients in the -convergence of some elliptic equations
We study the behavior of the solutions of the linear Dirichlet problems
with respect to perturbations
of the matrix (with respect to the -convergence) and with respect to
perturbations of the nonnegative coefficient and of the right hand side
satisfying the condition
Renormalized solutions of elliptic equations with general measure data
We study existence and (in some case) uniqueness for elliptic equations with measure data
The maximum cardinality of minimal inversion complete sets in finite reflection groups
We compute for reflection groups of type A,B,D,F4,H3 and for dihedral groups a statistic counting the maximal cardinality of a set of elements in the group whose generalized inversions yield the full set of inversions and which are minimal with respect to this property. We also provide lower bounds for the E types that we conjecture to be the exact value of our statistic
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