# 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.

## 3,076 Citations

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

- Mathematics
- 2004

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

- Mathematics
- 1977

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

- MathematicsInt. J. Syst. Sci.
- 2008

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

- Mathematics
- 2019

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

- Mathematics
- 2002

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

- Mathematics
- 2001

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

- Mathematics
- 2008

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

- Mathematics
- 2008

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

- Mathematics, Philosophy
- 2002

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

- Mathematics
- 2014

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…