A Regularity Theory for Variational Problems with Higher Order Derivatives
نویسندگان
چکیده
منابع مشابه
Multiobjective Duality in Variational Problems with Higher Order Derivatives
A multiobjective variational problem involving higher order derivatives is considered and optimality conditions for this problem are derived. A Mond-Weir type dual to this problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the al...
متن کاملHigher Order Variational Problems
Higher order variational problems appear often in the engineering literature and in connection with the so-called gradient theories of phase transitions within elasto-plastic regimes. The study of equilibria of micromagnetic materials asks for mastery of second order energies (see [51], [91]; see also [31], [38], [44], [45], [61], [77], [78], [79], [108]), and the Blake-Zisserman model for imag...
متن کاملPartial Regularity For Higher Order Variational Problems Under Anisotropic Growth Conditions
We prove a partial regularity result for local minimizers u : Rn ⊃ Ω → RM of the variational integral J(u,Ω) = ∫ Ω f(∇ku) dx, where k is any integer and f is a strictly convex integrand of anisotropic (p, q)–growth with exponents satisfying the condition q < p(1 + 2 n). This is some extension of the regularity theorem obtained in [BF2] for the case n = 2.
متن کاملOn Efficiency Conditions for Multiobjective Variational Problems Involving Higher Order Derivatives∗
This paper aims to formulate and prove necessary and sufficient conditions of efficiency for a class of multiobjective variational problems involving higher order derivatives. Consider a multiobjective optimization problem of minimizing a vector of simple integral functionals subject to certain higher order differential equations and/or inequations. We establish sufficient efficiency conditions...
متن کاملHigher-Order Difference and Higher-Order Splitting Methods for 2D Parabolic Problems with Mixed Derivatives
In this article we discuss a combination between fourth-order finite difference methods and fourth-order splitting methods for 2D parabolic problems with mixed derivatives. The finite difference methods are based on higher-order spatial discretization methods, whereas the timediscretization methods are higher-order discretizations using CrankNicolson or BDF methods. The splitting methods are hi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1990
ISSN: 0002-9947
DOI: 10.2307/2001759