Examples of classically unsolvable regular scalar variational problems satisfying standard growth conditions

1996 ◽  
Vol 37 (6) ◽  
pp. 1212-1227 ◽  
Author(s):  
M. A. Sychëv
Keyword(s):  
Variational Problems ◽  
Growth Conditions

scholarly journals Lipschitz Bounds and Nonautonomous Integrals

2021 ◽  
Author(s):  
Cristiana De Filippis ◽  
Giuseppe Mingione
Keyword(s):  
Variational Problems ◽  
Growth Conditions ◽  
Regularity Criteria ◽  
Regularity Of Solutions ◽  
Optimal Regularity ◽  
Lipschitz Regularity ◽  
Elliptic Case ◽  
Different Types ◽  
Vector Valued

AbstractWe provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems.

Hyperjacobians, determinantal ideals and weak solutions to variational problems

1983 ◽  
Vol 95 (3-4) ◽  
pp. 317-340 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Variational Problems ◽  
Growth Conditions ◽  
Higher Order ◽  
Symbolic Powers ◽  
Determinantal Ideals ◽  
Higher Dimensional ◽  
Existence Of Minimizers ◽  
Special Cases ◽  
Classical Invariant

SynopsisThe problem of classifying homogeneous null Lagrangians satisfying an nth order divergence identity is completely solved. All such differential polynomials are affine combinations of higher order Jacobian determinants, called hyperjacobians, which can be expressed as higher dimensional determinants of higher order Jacobian matrices. Special cases, called transvectants, are of importance in classical invariant theory. Transform techniques reduce this question to the characterization of the symbolic powers of certain determinantal ideals. Applications to the proof of existence of minimizers of certain quasi-convex variational problems with weakened growth conditions are discussed.

Influence of MBE Growth Conditions on Dislocation Densities of GaAs/Ge Epilayers Grown on Silicon Substrates

1985 ◽  
Vol 43 ◽  
pp. 364-365
Author(s):  
K.M. Hones ◽  
P. Sheldon ◽  
B.G. Yacobi ◽  
A. Mason
Keyword(s):  
High Efficiency ◽  
Lattice Mismatch ◽  
Low Cost ◽  
Growth Conditions ◽  
Nonradiative Recombination ◽  
Device Structure ◽  
Si Substrates ◽  
Transmission Electron ◽  
Dislocation Densities ◽  
Dislocation Type

There is increasing interest in growing epitaxial GaAs on Si substrates. Such a device structure would allow low-cost substrates to be used for high-efficiency cascade- junction solar cells. However, high-defect densities may result from the large lattice mismatch (∼4%) between the GaAs epilayer and the silicon substrate. These defects can act as nonradiative recombination centers that can degrade the optical and electrical properties of the epitaxially grown GaAs. For this reason, it is important to optimize epilayer growth conditions in order to minimize resulting dislocation densities. The purpose of this paper is to provide an indication of the quality of the epitaxially grown GaAs layers by using transmission electron microscopy (TEM) to examine dislocation type and density as a function of various growth conditions. In this study an intermediate Ge layer was used to avoid nucleation difficulties observed for GaAs growth directly on Si substrates. GaAs/Ge epilayers were grown by molecular beam epitaxy (MBE) on Si substrates in a manner similar to that described previously.

Diffraction from arrays of antiphase boundaries in ordered III-V alloys

1987 ◽  
Vol 45 ◽  
pp. 312-313
Author(s):  
T. S. Kuan
Keyword(s):  
High Surface ◽  
Growth Conditions ◽  
Ternary Alloys ◽  
Local Growth ◽  
Antiphase Boundaries ◽  
Surface Mobility ◽  
Ordered Phases ◽  
Diffraction Patterns ◽  
Atomically Flat ◽  
Degree Of Order

Recent electron diffraction studies have found ordered phases in AlxGa1-xAs, GaAsxSb1-x, and InxGa1-xAs alloy systems, and these ordered phases are likely to be found in many other III-V ternary alloys as well. The presence of ordered phases in these alloys was detected in the diffraction patterns through the appearance of superstructure reflections between the Bragg peaks (Fig. 1). The ordered phase observed in the AlxGa1-xAs and InxGa1-xAs systems is of the CuAu-I type, whereas in GaAsxSb1-x this phase and a chalcopyrite type ordered phase can be present simultaneously. The degree of order in these alloys is strongly dependent on the growth conditions, and during the growth of these alloys, high surface mobility of the depositing species is essential for the onset of ordering. Thus, the growth on atomically flat (110) surfaces usually produces much stronger ordering than the growth on (100) surfaces. The degree of order is also affected by the presence of antiphase boundaries (APBs) in the ordered phase. As shown in Fig. 2(a), a perfectly ordered In0.5Ga0.5As structure grown along the <110> direction consists of alternating InAs and GaAs monolayers, but due to local growth fluctuations, two types of APBs can occur: one involves two consecutive InAs monolayers and the other involves two consecutive GaAs monolayers.

The value of Electron Microscope studies of imperfect natural diamonds

1990 ◽  
Vol 48 (4) ◽  
pp. 194-195
Author(s):  
J C Walmsley ◽  
A R Lang
Keyword(s):  
Electron Microscope ◽  
Classification Scheme ◽  
Natural Diamond ◽  
Sudden Change ◽  
Growth Conditions ◽  
Diamond Growth ◽  
Major Constituent ◽  
Natural Diamonds ◽  
Type Ia ◽  
Platelet Defects

Interest in the defects and impurities in natural diamond, which are found in even the most perfect stone, is driven by the fact that diamond growth occurs at a depth of over 120Km. They display characteristics associated with their origin and their journey through the mantle to the surface of the Earth. An optical classification scheme for diamond exists based largely on the presence and segregation of nitrogen. For example type Ia, which includes 98% of all natural diamonds, contain nitrogen aggregated into small non-paramagnetic clusters and usually contain sub-micrometre platelet defects on {100} planes. Numerous transmission electron microscope (TEM) studies of these platelets and associated features have been made e.g. . Some diamonds, however, contain imperfections and impurities that place them outside this main classification scheme. Two such types are described.First, coated-diamonds which possess gem quality cores enclosed by a rind that is rich in submicrometre sized mineral inclusions. The transition from core to coat is quite sharp indicating a sudden change in growth conditions, Figure 1. As part of a TEM study of the inclusions apatite has been identified as a major constituent of the impurity present in many inclusion cavities, Figure 2.

Sign in / Sign up

Export Citation Format

Share Document