排序方式: 共有9条查询结果,搜索用时 15 毫秒
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Alexander I. Nazarov 《Journal of Global Optimization》2008,40(1-3):289-303
We describe recent results on attainability of sharp constants in the Sobolev inequality, the Sobolev–Poincaré inequality,
the Hardy–Sobolev inequality and related inequalities. This gives us the solvability of boundary value problems to critical
Emden–Fowler equations.
相似文献
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Michela Eleuteri 《Journal of Mathematical Analysis and Applications》2008,344(2):1120-1142
We prove regularity results for minimizers of functionals in the class , where is a fixed function and f is quasiconvex and fulfills a growth condition of the type
L−1|z|p(x)?f(x,ξ,z)?L(1+|z|p(x)), 相似文献
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L. Esposito G. Mingione 《NoDEA : Nonlinear Differential Equations and Applications》2000,7(1):107-125
We prove -partial regularity of minimizers with for a class of convex integral functionals with nearly linear growth whose model is In this way we extend to any dimension n a previous, analogous, result in [FS] valid only in the case
Received December 1998 相似文献
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We show the existence of a smooth spherical surface minimizing the Willmore functional subject to an area constraint in a compact Riemannian three-manifold, provided the area is small enough. Moreover, we partially classify complete surfaces of Willmore type with positive mean curvature in Riemannian three-manifolds. 相似文献
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Shibo Liu 《Journal of Mathematical Analysis and Applications》2006,316(1):229-236
We obtain multiple nonzero solutions for coercive p-Laplacian equations. In order to obtain the third nonzero solution, we use the second deformation lemma to construct the desired mountain pass path. 相似文献
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Davide L. Ferrario 《Advances in Mathematics》2007,213(2):763-784
Periodic and quasi-periodic solutions of the n-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries fulfills certain conditions (such as the rotating circle property). Here we generalize such conditions to more general group types and show how to constructively classify all groups satisfying such hypothesis, by a decomposition into irreducible transitive components. As examples we show approximate trajectories of some of the resulting symmetric minimizers. 相似文献
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We consider the two dimensional gravitational Vlasov–Poisson system. Using variational methods, we prove the existence of stationary solutions of minimal energy under a Casimir type constraint. The method also provides a stability criterion of these solutions for the evolution problem. 相似文献
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Juha Kinnunen Nageswari Shanmugalingam 《Transactions of the American Mathematical Society》2006,358(1):11-37
We show that if is a proper metric measure space equipped with a doubling measure supporting a Poincaré inequality, then subsets of with zero -capacity are precisely the -polar sets; that is, a relatively compact subset of a domain in is of zero -capacity if and only if there exists a -superharmonic function whose set of singularities contains the given set. In addition, we prove that if is a -hyperbolic metric space, then the -superharmonic function can be required to be -superharmonic on the entire space . We also study the the following question: If a set is of zero -capacity, does there exist a -superharmonic function whose set of singularities is precisely the given set?
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