scholarly journals On the regularity of solutions of one-dimensional variational obstacle problems

2018 ◽  
Vol 11 (2) ◽  
pp. 203-222 ◽  
Author(s):  
Jean-Philippe Mandallena
Keyword(s):  
Partial Regularity ◽  
Direct Method ◽  
Variational Problems ◽  
Obstacle Problems ◽  
Regularity Of Solutions ◽  
Hölder Continuous ◽  
One Dimensional ◽  
A Direct Method

AbstractWe study the regularity of solutions of one-dimensional variational obstacle problems in {W^{1,1}} when the Lagrangian is locally Hölder continuous and globally elliptic. In the spirit of the work of Sychev [5, 6, 7], a direct method is presented for investigating such regularity problems with obstacles. This consists of introducing a general subclass {\mathcal{L}} of {W^{1,1}}, related in a certain way to one-dimensional variational obstacle problems, such that every function of {\mathcal{L}} has Tonelli’s partial regularity, and then to prove that, depending on the regularity of the obstacles, solutions of corresponding variational problems belong to {\mathcal{L}}. As an application of this direct method, we prove that if the obstacles are {C^{1,\sigma}}, then every Sobolev solution has Tonelli’s partial regularity.

scholarly journals On a direct method for the determination of an exact invariant for the time-dependent harmonic oscillator

1977 ◽  
Vol 20 (1) ◽  
pp. 97-105 ◽  
Author(s):  
P. G. L. Leach
Keyword(s):  
Direct Method ◽  
Dynamical Symmetry ◽  
Time Dependent ◽  
Symmetry Groups ◽  
New Approach ◽  
One Dimensional ◽  
The One ◽  
A Direct Method ◽  
Exact Invariant

AbstractAn exact invariant is found for the one-dimensional oscillator with equation of motion . The method used is that of linear canonical transformations with time-dependent coeffcients. This is a new approach to the problem and has the advantage of simplicity. When f(t) and g(t) are zero, the invariant is related to the well-known Lewis invariant. The significance of extension to higher dimension of these results is indicated, in particular for the existence of non-invariance dynamical symmetry groups.

Single-Term Walsh Series Direct Method for the Solution of Nonlinear Problems in the Calculus of Variations

2004 ◽  
Vol 10 (7) ◽  
pp. 1071-1081 ◽  
Author(s):  
M. Razzaghi ◽  
B. Sepehrian
Keyword(s):  
Calculus Of Variations ◽  
Nonlinear Problem ◽  
Direct Method ◽  
Nonlinear Problems ◽  
Variational Problems ◽  
Walsh Series ◽  
Algebraic Equations ◽  
Brachistochrone Problem ◽  
Single Term ◽  
A Direct Method

A direct method for solving variational problems using single-term Walsh series is presented. Two nonlinear examples are considered. In the first example the classical brachistochrone problem is examined. and in the second example a higher-order nonlinear problem is considered. The properties of single-term Walsh series are given and are utilized to reduce the calculus of variations problems to the solution of algebraic equations. The method is general, easy to implement and yields accurate results.

Crystal Structure of an Ammonium Dithiocyanatocuprate(I) Complex with 18-Crown-6, [NH4(18-Crown-6){Cu(NCS)2}] Obtained from Zero Valent Metal

1997 ◽  
Vol 52 (11) ◽  
pp. 1311-1314 ◽  
Author(s):  
Julia A. Manskaya ◽  
Volodimir N. Kokozay ◽  
Konstantin V. Domasevitch
Keyword(s):  
Crystal Structure ◽  
Direct Method ◽  
Orthorhombic Space Group ◽  
Space Group ◽  
One Dimensional ◽  
X Ray ◽  
X Ray Crystallography ◽  
A Direct Method

The new macrocyclic dithiocyanatocuprate(I) complex [NH4(18-crown-6){Cu(NCS)2}] has been prepared using a direct method of interaction and characterized by X-ray crystallography (orthorhombic, space group Cmc21, with a = 12.453(2), b = 21.650(4), c = 8.151(2) Å, V = 2197.6(8) Å3, Z = 4 , R1 (F) = 0.054; wR2(F2) = 0.141 for 972 unique reflections with I > 2σ(I) and R1(F) = 0.082; w/?2(F2) = 0.210 for all 1098 unique reflections). The lattice comprises complex cations [NH4(18-crown-6)]+ and infinite polymeric anions [Cu(NCS)2]- of a one-dimensional zig-zag structure. The copper atoms adopt three-fold coordination [CuN2S] (Cu-N 1,89( 1), 1,90( 1) Å; Cu-S 2.278(4) Å).

Direct numerical method for isoperimetric fractional variational problems based on operational matrix

2017 ◽  
Vol 24 (14) ◽  
pp. 3063-3076 ◽  
Author(s):  
Samer S Ezz–Eldien ◽  
Ali H Bhrawy ◽  
Ahmed A El–Kalaawy
Keyword(s):  
Direct Method ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Variational Problems ◽  
Test Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Direct Numerical Method ◽  
Fractional Variational Problems ◽  
A Direct Method

In this paper, we applied a direct method for a solution of isoperimetric fractional variational problems. We use shifted Legendre orthonormal polynomials as basis function of operational matrices of fractional differentiation and fractional integration in combination with the Lagrange multipliers technique for converting such isoperimetric fractional variational problems into solving a system of algebraic equations. Also, we show the convergence analysis of the presented technique and introduce some test problems with comparisons between our numerical results with those introduced using different methods.

Partial regularity of solution to generalized Navier-Stokes problem

2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Václav Mácha
Keyword(s):  
Partial Regularity ◽  
Stokes Problem ◽  
Regularity Of Solutions ◽  
Navier Stokes ◽  
Singular Set ◽  
Hölder Continuous ◽  
Indirect Approach ◽  
Regularity Of Solution ◽  
Dimension 2 ◽  
Deviatoric Part

AbstractIn the presented work, we study the regularity of solutions to the generalized Navier-Stokes problem up to a C 2 boundary in dimensions two and three. The point of our generalization is an assumption that a deviatoric part of a stress tensor depends on a shear rate and on a pressure. We focus on estimates of the Hausdorff measure of a singular set which is defined as a complement of a set where a solution is Hölder continuous. We use so-called indirect approach to show partial regularity, for dimension 2 we get even an empty set of singular points.

scholarly journals Partial regularity up to the boundary for solutions of subquadratic elliptic systems

2018 ◽  
Vol 7 (4) ◽  
pp. 469-483 ◽  
Author(s):  
Zhong Tan ◽  
Yanzhen Wang ◽  
Shuhong Chen
Keyword(s):  
Partial Regularity ◽  
Direct Method ◽  
Elliptic Systems ◽  
Divergence Form ◽  
Singular Set ◽  
Nonlinear Elliptic Systems ◽  
Hölder Continuous ◽  
Nonlinear Elliptic ◽  
Controllable Growth Condition ◽  
Controllable Growth

AbstractIn this paper, we are concerned with the nonlinear elliptic systems in divergence form under controllable growth condition. We prove that the weak solution u is locally Hölder continuous besides a singular set by using the direct method and classical Morrey-type estimates. Here the Hausdorff dimension of the singular set is less than {n-p}. This result not only holds in the interior, but also holds up to the boundary.

Sign in / Sign up

Export Citation Format

Share Document