On the Hardy-Sobolev-Maz’ya inequality and its generalizations
نویسندگان
چکیده
The paper deals with natural generalizations of the Hardy-SobolevMaz’ya inequality and some related questions, such as the optimality and stability of such inequalities, the existence of minimizers of the associated variational problem, and the natural energy space associated with the given functional. 2000 Mathematics Subject Classification. 35J20, 35J60, 35J70, 49R50.
منابع مشابه
Hardy-sobolev-maz’ya Inequalities for Arbitrary Domains
1.1. Hardy-Sobolev-Maz’ya inequalities. Hardy inequalities and Sobolev inequalities bound the size of a function, measured by a (possibly weighted) L norm, in terms of its smoothness, measured by an integral of its gradient. Maz’ya [22] proved that for functions on the half-space R+ = {x ∈ R : xN > 0}, N ≥ 3, which vanish on the boundary, the sharp version of the Hardy inequality can be combine...
متن کاملm at h . A P ] 2 4 A ug 2 00 5 Minimizers for the Hardy - Sobolev - Maz ’ ya inequality
We show existence of minimizers for the Hardy-Sobolev-Maz’ya inequality in Rm+n \ Rn when either m > 2, n ≥ 1 or m = 1, n ≥ 3. The authors expresses their gratitude to the faculties of mathematics department at Technion Haifa Institute of Technology and of the University of Cyprus for their hospitality. A.T. acknowledges partial support by the RTN European network Fronts–Singularities, HPRN-CT-...
متن کامل1 N ov 2 00 5 On existence of minimizers for the Hardy - Sobolev - Maz ’ ya inequality
We show existence of minimizers for the Hardy-Sobolev-Maz’ya inequality in Rm+n \ Rn when either m > 2, n ≥ 1 or m = 1, n ≥ 3. The authors expresses their gratitude to the faculties of mathematics departments at Technion Haifa Institute of Technology, at the University of Crete and of the University of Cyprus for their hospitality. A.T. acknowledges partial support by the RTN European network F...
متن کاملOn Hardy-sobolev Embedding
1. Interpolation inequalities. A classical problem in analysis is to understand how “smoothness” controls norms that measure the “size” of functions. Maz’ya recognized in his classic text on Sobolev spaces the intrinsic importance of inequalities that would refine both Hardy’s inequality and Sobolev embedding. Dilation invariance and group symmetry play an essential role in determining sharp co...
متن کاملGeneral Hardy-Type Inequalities with Non-conjugate Exponents
We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008