| 继第一版出版十八年再次全新呈现 仅500多条参考书目就将其价值大大提升 |
| 《变分法(第4版)》 chapter i.the direct methods in the calculus of variations 1.lower semi-continuity degenerate elliptic equations, 4 —minimal partitioning hypersurfaces, 6 —minimal hypersurfaces in riemannian manifolds, 7 —a general lower semi-continuity result, 8 2.constraints semilinear elliptic boundary value problems, 14 —perron's method in a variational guise, 16 —the classical plateau problem, 19 3.compensated compactness applications in elasticity, 29 —convergence results for nonlinear elliptic equations, 32 —hardy space methods, 35 4.the concentration-compactness principle existence of extremal functions for sobolev embeddings, 42 5.ekeland's variational principle existence of minimizers for quasi-convex functionals, 54 6.duality hamiltonian systems, 60 —periodic solutions of nonlinear wave equations, 65 7.minimization problems depending on parameters harmonic maps with singularities, 71 chapter ii.minimax methods 1.the finite dimensional case 2.the palais-smale condition 3.a general deformation lemma .pseudo-gradient flows on banach spaces, 81 —pseudo-gradient flows on manifolds, 85 4.the minimax principle closed geodesics on spheres, 89 5.index theory krasnoselskii genus, 94 —minimax principles for even functionals, 96 —applications to semilinear elliptic problems, 98 —general index theories, 99 —ljusternik-schnirelman category, 100 —a geometrical si-index, 101 —multiple periodic orbits of hamiltonian systems, 103 6.the mountain pass lemma and its variants applications to semilinear elliptic boundary value problems, 110 —the symmetric mountain pass lemma, 112 —application to semilinear equa- tions with symmetry, 116 7.perturbation theory applications to semilinear elliptic equations, 120 8.linking applications to semilinear elliptic equations, 128 —applications to hamil- tonian systems, 130 9.parameter dependence 10.critical points of mountain pass type multiple solutions of coercive elliptic problems, 147 11.non-differentiable fhnctionals 12.ljnsternik-schnirelman theory on convex sets applications to semilinear elliptic boundary value problems, 166 chapter iii.limit cases of the palais-smale condition 1.pohozaev's non-existence result 2.the brezis-nirenberg result constrained minimization, 174 —the unconstrained case: local compact- ness, 175 —multiple solutions, 180 3.the effect of topology a global compactness result, 184 —positive solutions on annular-shaped regions, 190 4.the yamabe problem the variational approach, 195 —the locally conformally flat case, 197 —the yamabe flow, 198 —the proof of theorem 4.9 (following ye [1]), 200 —convergence of the yamabe flow in the general case, 204 —the compact case ucc ] 0, 211 —bubbling: the casu∞ 0,216 5.the dirichlet problem for the equation of constant mean curvature small solutions, 221 —the volume functional, 223 - wente's uniqueness result, 225 —local compactness, 226 —large solutions, 229 6.harmonic maps of riemannian surfaces the euler-lagrange equations for harmonic maps, 232 —bochner identity, 234 —the homotopy problem and its functional analytic setting, 234 —existence and non-existence results, 237 —the heat flow for harmonic maps, 238 —the global existence result, 239 —the proof of theorem 6.6, 242 —finite-time blow-up, 253 —reverse bubbling and nonuniqueness, 257 appendix a sobolev spaces, 263 —hslder spaces, 264 —imbedding theorems, 264 —density theorem, 265 —trace and extension theorems, 265 —poincar4 inequality, 266 appendix b schauder estimates, 268 —lp-theory, 268 —weak solutions, 269 —a reg- ularity result, 269 —maximum principle, 271 —weak maximum principle, 272 —application, 273 appendix c frechet differentiability, 274 —natural growth conditions, 276 references index |
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