Multiple Integrals in the Calculus of Variations

@inproceedings{Morrey1966MultipleII,
  title={Multiple Integrals in the Calculus of Variations},
  author={Charles Bradfield Morrey},
  year={1966}
}
Semi-classical results.- The spaces Hmp and Hmp0.- Existence theorems.- Differentiability of weak solutions.- Regularity theorems for the solutions of general elliptic systems and boundary value problems.- A variational method in the theory of harmonic integrals.- The -Neumann problem on strongly pseudo-convex manifolds.- to parametric Integrals two dimensional problems.- The higher dimensional plateau problems. 
View via Publisher
download.e-bookshelf.de
3,076 Citations
Highly Influential Citations
280
Background Citations
768
Methods Citations
236
Results Citations
48

3,076 Citations

Singular Integral Operators, Morrey Spaces and Fine Regularity of Solutions to PDE's

Boundedness in Morrey spaces is studied for singular integral operators with kernels of mixed homogeneity and their commutators with multiplication by a BMO-function. The results are applied in…

Multiple integrals of Lipschitz functions in the calculus of variations

We consider a multiple integral problem in the calculus of variations in which the integrand is locally Lipschitz but not differentiable, and in which minimization takes place over a Sobolev space.…

Regularity of solutions to higher-order integrals of the calculus of variations

The main regularity result asserts that autonomous integral functionals with a Lagrangian having coercive partial derivatives with respect to the higher-order derivatives admit only minimisers with essentially bounded derivatives.

On the polyharmonic Neumann problem in weighted spaces

ABSTRACT We study the unique (non-unique) solvability of the Neumann problem for the polyharmonic equation in unbounded domains under the assumption that a generalized solution of this problem has a…

Nonlinear elliptic systems with Dini continuous coefficients

Abstract. We consider nonlinear elliptic systems of divergence type with Dini continous coefficients and prove a partial regularity result for weak solutions. Our method of proof is based on a…

Sobolev spaces and approximation problems for differential operators

In this paper we give an introduction to the theory of Sobolev spaces, and discuss the connection between these spaces and certain approximation problems associated with elliptic differential…

Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries

Here we study the asymptotic limits of solutions of some singularly perturbed elliptic systems. The limiting problems involve multiple valued harmonic functions or, in general, harmonic maps to…

Regularity for quasi-linear elliptic systems with discontinuous coefficients

In this paper we study regularity and partial regularity for the weak solution of a class of general quasi-linear elliptic equations and systems, which are of the quasi-linear main coecien ts…

ON SOLUTIONS OF THE DIRICHLET PROBLEM FOR A CLASS OF PARTIAL DIFFERENTIAL INCLUSIONS WITH SUPERLINEAR NONLINEARITIES

ABSTRACT We investigate the existence and properties of solutions of the Dirichlet problem for the following differential inclusion for a.e. y∈Ω, being a generalized Euler–Lagrange equation for where…

Hölder regularity for weak solutions of diagonal divergence quasilinear degenerate elliptic systems

In this paper, we establish Holder regularity for weak solutions of a class of diagonal divergence quasilinear degenerate elliptic systems of Hormander's vector fields when the coefficients belong to…
...