Download Analysis of Hamiltonian PDEs by Kuksin, Sergej B PDF

By Kuksin, Sergej B

For the final 20-30 years, curiosity between mathematicians and physicists in infinite-dimensional Hamiltonian structures and Hamiltonian partial differential equations has been turning out to be strongly, and plenty of papers and a few books were written on integrable Hamiltonian PDEs. over the last decade although, the curiosity has shifted progressively in the direction of non-integrable Hamiltonian PDEs. the following, now not algebra yet research and symplectic geometry are definitely the right analysing instruments. the current booklet is the 1st one to take advantage of this method of Hamiltonian PDEs and current a whole evidence of the "KAM for PDEs" theorem. will probably be a useful resource of data for postgraduate arithmetic and physics scholars and researchers.

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V. G. Maz'ya, "Classes of sets and measures that are connected with imbedding theorems," in: Imbedding Theorems and Their Applications, (Proceedings of a Symposium, Baku 1966), [in Russian], Nauka, Moscow (1970), pp. 142-159, 246. J. -L. Lions, "Spaces of the Beppo Levi type," Ann. Inst. Fourier, ~, 305- 2. 3. 37O (1955). 5. V. G. Maz'ya, "On weak solutions of the Dirichlet and Neumann problems," Tr. Mosk. Mat. , 20, 137-172 (1969). V. G. Maz'ya, "On the Neumann problem in regions with nonregular boundaries," Sib.

1322-1350 (1968). E. Gagliardo, "Properties of certain classes of functions of several variables," Ricerche Mat. , No. I, 102-137 (1958). G. H. Hardy, J. E. Littlewood, and G. Polya, "Some simple inequalities satisfied by convex functions," Messenger Math. 58, No. I0, 142-152, (1929). S. L. Sobolev, "On certain theorems of functional analysis," Mat. , 4 (46), No. 3, 471-498 (1938). 6. 7. 8. 9. 95 V. G. Maz'ya i~ Basic Notation. ~ + ~'~ E ~ . with compact closure 0 be a point on the curve ~ ' ~ ~ , and , and suppose that We consider the elliptic operator 2 in ~'~ , where the be a subdomain of ~ 2 # 2 # G~j- are functions that satisfy a Lipschitz condition in a positive-definite matrix, and the a[ and ~ ~ and form are bounded measurable functions.

No. 29-50 (1976). V. G. Maz'ya, "Classes of sets and measures that are connected with imbedding theorems," in: Imbedding Theorems and Their Applications, (Proceedings of a Symposium, Baku 1966), [in Russian], Nauka, Moscow (1970), pp. 142-159, 246. J. -L. Lions, "Spaces of the Beppo Levi type," Ann. Inst. Fourier, ~, 305- 2. 3. 37O (1955). 5. V. G. Maz'ya, "On weak solutions of the Dirichlet and Neumann problems," Tr. Mosk. Mat. , 20, 137-172 (1969). V. G. Maz'ya, "On the Neumann problem in regions with nonregular boundaries," Sib.

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