Uniqueness for a semilinear elliptic equation in non-contractible domains under supercritical growth conditions.
Rank-one connections at infinity and quasiconvex hulls.
Some constancy results for harmonic maps from non-contractable domains into spheres.
On some quasiconvex functions with linear growth.
On variational approach to photometric stereo
On the quasiconvex exposed points
The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.
An approximation theorem for sequences of linear strains and its applications
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in by the sequence of linear strains of mapping bounded in Sobolev space . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.
Quasiconvex functions, and two elastic wells
Compensated convexity and its applications
On the structure of quasiconvex hulls
A construction of quasiconvex functions with linear growth at infinity
On the quasiconvex exposed points
The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.
An approximation theorem for sequences of linear strains and its applications
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in by the sequence of linear strains of mapping bounded in Sobolev space . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains a construction of quasiconvex functions with linear growth.
Instability of the eikonal equation and shape from shading
An evolutionary double-well problem
Instability of the eikonal equation and shape from shading
In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation on a domain in . Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms. ...
Global higher integrability of jacobians on bounded domains
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