A smooth transonic flow problem is formulated as follows: for a de Laval nozzle, one looks
for a smooth transonic flow of Meyer type whose sonic points are all exceptional and whose …

This paper concerns properties of sonic curves for two-dimensional smooth subsonic-sonic
and transonic steady potential flows, which are governed by quasi-linear degenerate elliptic …

We survey recent developments on the analysis of Gauss--Codazzi--Ricci equations, the first-
order PDE system arising from the classical problem of isometric immersions in differential …

In this paper, the method of compensated compactness is applied to the problem of
isometric immersion of a two-dimensional Riemannian manifold with negative Gauss …

In this paper, we study the smooth isometric immersion of a complete simply connected
surface with a negative Gauss curvature in the three-dimensional Euclidean space. For a …

We formulate and prove compensated compactness theorems concerning the limiting
behaviour of wedge products of weakly convergent differential forms on closed Riemannian …

We study the weak continuity of two interrelated non-linear partial differential equations, the
Yang-Mills equations and the Gau {\ss}-Codazzi-Ricci equations, involving $ L^ p …

This thesis is a study of problems related to isometric immersions of Riemannian manifolds
in Euclidean space. We address three main questions: the weak continuity of geometric …

The isometric immersion of two-dimensional Riemannian manifolds with negative Gauss
curvature into the three-dimensional Euclidean space is considered through the Gauss …

We prove uniqueness of smooth isometric immersions within the class of negatively curved
corrugated two-dimensional immersions embedded into $\mathbb {R}^ 3$. The main tool we …