# A priori estimates and existence for quasi-linear elliptic equations

## Related Articles

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Presents a study which used an extension of quasilinearization to differential equations with a parameter. Purpose of the study; Theorems and proofs; Main result.

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This paper concerns a quasilinear system involving the operator curl. This system is an approximation of the anisotropic Ginzburgâ€“Landau system which describes the Meissner state of type II superconductors. The existence of the weak solutions of the quasilinear system is proved by...

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We show a regularity criterion to the harmonic heat flow from 2-dimensional Riemannian manifold M into a sphere. It is shown that a weak solution of the harmonic heat flow from 2-dimensional manifold into a sphere is regular under the criterion where BMO r is the space of bounded mean...

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In this paper we study the limit, in the sense of the G-convergence, of sequences of two-dimensional energies of the type $${\int_\Omega A_n\nabla u\cdot\nabla u\,dx+\int_\Omega u^2d\mu_n}$$ , where A n is a symmetric positive definite matrix-valued function and ï¿½ n is a nonnegative...

- The dynamics of elastic closed curves under uniform high pressure. Okabe, Shinya // Calculus of Variations & Partial Differential Equations;Dec2008, Vol. 33 Issue 4, p493
We consider the dynamics of an inextensible elastic closed wire in the plane under uniform high pressure. In 1967, Tadjbakhsh and Odeh (J. Math. Anal. Appl. 18:59ï¿½74, 1967) posed a variational problem to determine the shape of a buckled elastic ring under uniform pressure. In order to...

- Two surprising maximisation problems. LORD, NICK // Mathematical Gazette;Nov2013, Vol. 97 Issue 540, p535
The article presents two surprising problems on maximisation.

- Blow-up Mechanism of Classical Solutions to Quasilinear Hyperbolic Systems in the Critical Case. Li, Tatsien; Wang, Libin // Chinese Annals of Mathematics;Jan2006, Vol. 27 Issue 1, p53
This paper deals with the blow-up phenomenon, particularly, the geometric blow-up mechanism, of classical solutions to the Cauchy problem for quasilinear hyperbolic systems in the critical case. We prove that it is still the envelope of the same family of characteristics which yields the blowup...

- Identification of the coefficient of the time derivative in a quasilinear parabolic equation. Fedus�, U. // Journal of Mathematical Sciences;Jul2010, Vol. 168 Issue 4, p523
We establish conditions for the existence and uniqueness of a solution of the inverse problem for a onedimensional quasilinear parabolic equation with an unknown coefficient of the time derivative in the case of boundary conditions of the second kind.