Symplectic structures related with higher order variational problems
نویسندگان
چکیده
منابع مشابه
Higher 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...
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where ∇w represents the tensor of all k order (weak) partial derivatives. Our main concern is the investigation of the smoothness properties of such local minimizers under suitable assumptions on the energy density f . For the first order case (i.e. k = 1) we have rather general results which can be found for example in the textbooks of Morrey [Mo], Ladyzhenskaya and Ural’tseva [LU], Gilbarg an...
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For Hamiltonian systems of the form H= T(p) + V(q) a method is shown to construct explicit and time reversible symplectic integrators of higher order. For any even order there exists at least one symplectic integrator with exact coefficients. The simplest one is the 4th order integrator which agrees with one found by Forest and by Ned. For 6th and 8th orders, symplectic integrators with fewer s...
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ژورنال
عنوان ژورنال: International Journal of Geometric Methods in Modern Physics
سال: 2015
ISSN: 0219-8878,1793-6977
DOI: 10.1142/s021988781550084x