Calculus of Variations Smooth solutions to a class of mixed type Monge-Ampère equations

Abstract We prove the existence of C ∞ local solutions to a class of mixed type MongeAmpère equations in the plane. More precisely, the equation changes type to finite order across two smooth curves intersecting transversely at a point. Existence of C ∞ global solutions to a corresponding class of linear mixed type equations is also established. These results are motivated by and may be applied to the problem of prescribed Gaussian curvature for graphs, the isometric embedding problem for 2-dimensional Riemannian manifolds into Euclidean 3-space, and also transonic fluid flow. Mathematics Subject Classification 35M10 · 53A0

Universal singular sets for one-dimensional variational problems

Summary. A study is made of the regularity properties of minimizers u of the integral x, u, u ) dx subject to the boundary conditions u(a) = o~, u(b) = r as the interval (a, b) and boundary values o~,/3 are varied. Under natural hypotheses on f it is shown that the set of points in the (x, u)-plane at which a minimizer u can have infinite derivative for some interval and boundary values is small in the sense of category

Isothermal and Cyclic Aging of 310S Austenitic Stainless Steel

Unusual damage and high creep strain rates have been observed on components made of 310S stainless steel subjected to thermal cycles between room temperature and 1143 K (870 °C). Microstructural characterization of such components after service evidenced high contents in sigma phase which formed first from δ-ferrite and then from γ-austenite. To get some insight into this microstructural evolution, isothermal and cyclic aging of 310S stainless steel has been studied experimentally and discussed on the basis of numerical simulations. The higher contents of sigma phase observed after cyclic agings than after isothermal treatments are clearly associated with nucleation triggered by thermal cycling

Evolving convex curves

Abstract. We consider the behaviour of convex curves undergoing curvaturedriven motion. In particular we describe the long-term behaviour of solutions and properties of limiting shapes, and prove existence of unique solutions from singular or non-strictly convex initial curves, with sharp regularity estimates