On the regularity of the minima of variational integrals
Mariano Giaquinta,Enrico Giusti +1 more
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This article is published in Acta Mathematica.The article was published on 1982-07-01 and is currently open access. It has received 478 citations till now. The article focuses on the topics: Variational integrator & Variational method.read more
Citations
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Journal ArticleDOI
The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
TL;DR: In this article, the natural generalization of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations is discussed. But the natural condition of uralization is not defined.
Journal ArticleDOI
Another Report on Harmonic Maps
James Eells,Luc Lemaire +1 more
TL;DR: In this paper, it was shown that a map (f>:{M,g)-+(N,h) between Riemannian manifolds which is continuous and of class L\\ is harmonic if and only if it is a critical point of the energy functional.
Journal ArticleDOI
Regularity Results for a Class of Functionals with Non-Standard Growth
Emilio Acerbi,Giuseppe Mingione +1 more
TL;DR: In this paper, the integral functional under non-standard growth assumptions was considered and the regularity of minimizers was proved under sharp assumptions on the continuous function p(x) > 1.
Journal ArticleDOI
Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions
Book
An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
TL;DR: In this article, the authors focus on the regularity theory for elliptic systems and illustrate some of the basic ideas and techniques introduced in this context, confining themselves to important but simple situations and refraining from completeness.
References
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Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
BookDOI
Multiple integrals in the calculus of variations
TL;DR: In this paper, a variational method in the theory of harmonic integrals has been proposed to solve the -Neumann problem on strongly pseudo-convex manifolds and parametric Integrals two-dimensional problems.
Book ChapterDOI
On elliptic partial differential equations
TL;DR: In this paper, a series of lectures on the theory of elliptic differential equations is presented, including the Hilbert space approach to the Dirichlet problem for strongly elliptic systems, and various inequalities.
Journal ArticleDOI
The Lp-integrability of the partial derivatives of A quasiconformal mapping
TL;DR: In this paper, it was shown that the maximum stretching and generalized Jacobian are locally L -integrable in D for p e [1, n + c] where c is a positive constant which depends only on K and n. The CalderonZygmund inequality was applied to the Hubert transform which relates the complex derivatives of a normalized plane quasiconformal mapping.