Class Of Elliptic Systems Research Articles

Uniform Hölder Estimates in a Class of Elliptic Systems and Applications to Singular Limits in Models for Diffusion Flames

The main result of this paper is a general Holder estimate in a class of singularly perturbed elliptic systems. This estimate is applied to the study of the well-known Burke–Schuman approximation in flame theory. After reviewing some classical cases (equidiffusional case; high activation energy approximation) we turn to the non-equidiffusional case, and to nonlinear diffusion models. The limiting problems are nonlinear elliptic equations; they have Holder or Lipschitz maximal global regularity. A natural question is then whether this regularity is kept uniformly throughout the approximation process, and we show that this is true in general.

A priori Estimates and Existence for Elliptic Systems via Bootstrap in Weighted Lebesgue Spaces

We present a new general method to obtain regularity and a priori estimates for solutions of semilinear elliptic systems in bounded domains. This method is based on a bootstrap procedure, used alternatively on each component, in the scale of weighted Lebesgue spaces Lpδ(Ω)=Lp(Ωδ(x) dx), where δ(x) is the distance to the boundary. Using this method, we significantly improve the known existence results for various classes of elliptic systems.

Solutions with prescribed number of nodes to superlinear elliptic systems

We consider a class of elliptic systems in the following form: − ΔU+U= ∇E(U), U(x)∈ R 2 with x∈ R N . We prove the existence of infinitely many solutions which are characterized by the number of nodes of each component. Our argument is based upon an extension of the results of Terracini and Verzini (Nonlinear Differential Equations Appl. 8 (2001) 323).

The existence of three nontrivial solutions of a class of elliptic systems

The existence of three nontrivial solutions of a class of elliptic systems

Multiplicity for symmetric indefinite functionals: applications to Hamiltonian and elliptic systems

In this article we study the existence of critical points for certain superquadratic strongly indefinite even functionals appearing in the study of periodic solutions of Hamiltonian systems and solutions of certain class of Elliptic Systems. We first present two abstract critical point theorems for even functionals. These results are well suited for our applications, but they are interesting by their own. These theorems are then applied to the specific problems we mentioned, when the corresponding Hamiltonians are superquadratic. Critical points theory for even indefinite functionals was studied by Benci in [2], where he developed a general pseudo index theory, a variant of the classical genus theory (c.f. [10]). We want to point out that our approach is totally different from [2]. Taking advantages of the even nature of the functional we shall construct a geometric linking structure which does not require conditions near the origin (see [10] for examples of some standard linking and compare the set up of our linking in Theorem 1.1).

Existence and representation of solutions of a class of elliptic systems of partial differential equations of first order in the space

We study the existence of solutions of the general elliptic system of partial differential equations in the space where the principal part may be represented with the help of a CLIFFORDalgebra 𝔄. We construct an integral representation and discuss the properties of the kernels.

A Cauchy integral formula for a class of elliptic systems of partial differential equations of first order in the space

This paper is a continuation of [6]. Here we construct a CAUCHY integral formula and a POMPEJU-representation for elliptic systems of partial differential equations of first order in Rn, which may be described with the help of a CLIFFORD-algebra. Moreover we study properties of the fundamental kernels and jump-integrals.

Function theory for a class of elliptic systems in the plane

Function theory for a class of elliptic systems in the plane