An estimate of the gap of the first two eigenvalues in the Schrödinger operator
An example of a nonlinear second order elliptic system in three dimension
We provide an explicit example of a nonlinear second order elliptic system of two equations in three dimension to compare two -regularity theories. We show that, for certain range of parameters, the theory developed in Daněček, Nonlinear Differential Equations Appl.9 (2002), gives a stronger result than the theory introduced in Koshelev, Lecture Notes in Mathematics,1614, 1995. In addition, there is a range of parameters where the first theory gives H"older continuity of solution for all , while...
An example of irregular solution to a nonlinear Euler-Lagrange elliptic system with real analytic coefficients
An existence and approximation theorem for solutions of degenerate quasilinear elliptic equations
The main result establishes that a weak solution of degenerate quasilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate quasilinear elliptic equations.
An existence and localization theorem for the solutions of a Dirichlet problem
We establish an existence theorem for a Dirichlet problem with homogeneous boundary conditions by using a general variational principle of Ricceri.
An existence result for a free boundary problem for the -Laplace operator.
An existence result for a quadrature surface free boundary problem
The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.
An existence result for a semipositone problem with a sign changing weight.
An existence result for an interior electromagnetic casting problem
This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.
An existence result for elliptic problems with singular critical growth.
An existence result for nonlinear elliptic problems involving critical Sobolev exponent
An existence theorem for a class of elliptic problems in L¹
We prove an existence result for solutions of some class of nonlinear elliptic problems having natural growth terms and L¹ data.
An existence theorem for a non-regular variational problem.
An existence theorem for a strongly nonlinear elliptic problem in Musielak-Orlicz spaces
We prove an existence result for some class of strongly nonlinear elliptic problems in the Musielak-Orlicz spaces , under the assumption that the conjugate function of φ satisfies the Δ₂-condition.
An existence theorem for the Yamabe problem on manifolds with boundary
Let be a compact Riemannian manifold with boundary. We consider the problem (first studied by Escobar in 1992) of finding a conformal metric with constant scalar curvature in the interior and zero mean curvature on the boundary. Using a local test function construction, we are able to settle most cases left open by Escobar’s work. Moreover, we reduce the remaining cases to the positive mass theorem.
An explicit formula for symmetric polynomials related to the eigenfunctions of Calogero-Sutherland models.
An explicit potential theory for the stokes resolvent boundary value problems in three dimensions.
An extension of a multiplicity theorem by Ricceri with an application to a class of quasilinear equations
A recent multiplicity result by Ricceri, stated for equations in Hilbert spaces, is extended to a wider class of Banach spaces. Applications to nonlinear boundary value problems involving the p-Laplacian are presented.
An Extrerior Mixed Boundary Value Problem for the Helmholtz Equation
An Hadamard maximum principle for the biplacian on hyperbolic manifolds
We prove the existence of a maximum principle for operators of the type , for weights with subharmonic. It is associated with certain simply connected subdomains that are produced by a Hele-Shaw flow emanating from a given point in the domain. For constant weight, these are the circular disks in the domain. The principle is equivalent to the following statement. THEOREM. Suppose is logarithmically subharmonic on the unit disk, and that the weight times area measure is a reproducing measure...