SOBOLEV CLASSES OF MAPPINGS ON A CARNOT–CARATH′EODORY SPACE: VARIOUS NORMS AND VARIATIONAL PROBLEMS

S. K. Vodop yanov; N. N. Romanovskii

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SOBOLEV CLASSES OF MAPPINGS ON A CARNOT–CARATH′EODORY SPACE: VARIOUS NORMS AND VARIATIONAL PROBLEMS

机译：Carnot-Carath杂波空间上映照的Sobolev类：各种范数和变问题

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摘要

We prove the equivalence of various definitions of Sobolev classes and the BV -class of metric-space-valued mappings on some domain in a Carnot–Carath′eodory space. Moreover, we prove the existence and uniqueness of the solution to some variational problem.

机译：我们证明了Carbo–Carath'eodory空间中某个域上Sobolev类的各种定义和度量空间值映射的BV类的等价性。此外，我们证明了某些变分问题解的存在性和唯一性。

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《Siberian Mathematical Journal》 |2008年第5期|共15页
作者
S. K. Vodop yanov; N. N. Romanovskii;
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正文语种 eng
中图分类数学;
关键词
Carnot–Carath′eodory space; Sobolev classes of mappings; variational problem;

机译：Carnot–Carath'气味空间;Sobolev映射类;变分问题;

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专利

1. SOBOLEV CLASSES OF MAPPINGS ON A CARNOT–CARATH′EODORY SPACE: VARIOUS NORMS AND VARIATIONAL PROBLEMS [J] . S. K. Vodop yanov, N. N. Romanovskii Siberian Mathematical Journal . 2008,第5期

机译：Carnot-Carath杂波空间上映照的Sobolev类：各种范数和变问题
2. Differentiability of the mappings of Carnot-Carathéodory spaces in the Sobolev and BV-topologies [J] . S. K. Vodop’yanov, D. V. Isangulova Siberian Mathematical Journal . 2007,第1期

机译：Sobolev和BV拓扑中Carnot-Carathéodory空间的映射的可微性
3. Hardy–Sobolev Type Inequalities with Sharp Constants in Carnot–Carathéodory Spaces [J] . Donatella Danielli, Nicola Garofalo, Nguyen Cong Phuc Potential Analysis . 2011,第3期

机译：Carnot-Carathéodory空间中具有尖锐常数的Hardy-Sobolev型不等式
4. WEAK MINIMA AND QUASIMINIMA OF VARIATIONAL INTEGRALS IN CARNOT-CARATH(E)ODORY SPACE [C] . LAN-RU HOU Boundary value problems, Integral equations and related problems. . 2010

机译：Carnot-Carath（E）气味空间中的积分的弱极小值和拟极小值
5. Sobolev norms of holomorphic sections and variations of the density of states [D] . Hanson, Nels 2008

机译：全同形截面的Sobolev范数和状态密度的变化
6. On the Normed Space of Equivalence Classes of Fuzzy Numbers [O] . Dong Qiu, Chongxia Lu, Wei Zhang 2013

机译：关于模糊数等价类的赋范空间
7. SOBOLEV CLASSES AND HORIZONTAL ENERGY MINIMIZERS BETWEEN CARNOT-CARATHÉODORY SPACES [O] . Kanghai Tan 2007

机译：CaRNOT-CaRaTHÉODORY空间中的sOBOLEV类和水平能量最小化

SOBOLEV CLASSES OF MAPPINGS ON A CARNOT–CARATH′EODORY SPACE: VARIOUS NORMS AND VARIATIONAL PROBLEMS

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