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1.ÌâÄ¿£ºL^p resolvent estimates for constant coefficient elliptic systems on Lipschitz domains ÆÚ¿¯£ºJournal of Functional Analysis ×÷ÕߣºWei Wei£¬Zhenqiu Zhang DOI£º10.1016/j.jfa.2014.08.010 2.ÌâÄ¿£ºModulation space estimates for Schrödinger type equations with time-dependent potentials ÆÚ¿¯£º Czechoslovak Mathematical Journal ×÷Õߣº Wei Wei DOI£º10.1007/s10587-014-0118-5 3.ÌâÄ¿£ºL^p resolvent estimates for variable coefficient elliptic systems on Lipschitz domains ÆÚ¿¯£º Analysis and Applications ×÷ÕߣºWei Wei£¬Zhenqiu Zhang DOI£º10.1142/S021953051450050X ·Ç³£¸Ðл£¡ |
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L-p resolvent estimates for constant coefficient elliptic systems on Lipschitz domains ×÷Õß:Wei, W (Wei, Wei); Zhang, ZQ (Zhang, Zhenqiu)[ 1 ] JOURNAL OF FUNCTIONAL ANALYSIS ¾í: 267 ÆÚ: 9 Ò³: 3262-3293 DOI: 10.1016/j.jfa.2014.08.010 ³ö°æÄê: NOV 1 2014 ²é¿´ÆÚ¿¯ÐÅÏ¢ ÕªÒª In this paper, we establish the L-P resolvent estimates on a Lipschitz domain Omega in R-d for constant coefficient elliptic systems with homogeneous Neumann boundary conditions, where 1 < p < infinity for d = 3, and 2d/(d + 3) - epsilon < p < 2d/(d - 3) + epsilon for d >= 4 with some positive constant epsilon = epsilon(Omega). We also give the global L-P estimates for the derivatives of solutions to the previous systems, where 2 <= p < 2d/(d - 1)+epsilon for d >= 3. Finally we extend our main results to the case of some variable coefficient elliptic systems on a bounded Lipschitz domain. (C) 2014 Elsevier Inc. All rights reserved. ¹Ø¼ü´Ê ×÷Õ߹ؼü´Ê:Resolvent estimates; Elliptic system; Lipschitz domain; Neumann problems KeyWords Plus:BOUNDARY-VALUE-PROBLEMS; LAYER POTENTIALS; NEUMANN PROBLEM; SPACES; EQUATION ×÷ÕßÐÅÏ¢ ͨѶ×÷ÕßµØÖ·: Zhang, ZQ (ͨѶ×÷Õß) ÏÔʾÔöÇ¿×éÖ¯ÐÅÏ¢µÄÃû³Æ Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China. µØÖ·: ÏÔʾÔöÇ¿×éÖ¯ÐÅÏ¢µÄÃû³Æ [ 1 ] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China ÏÔʾÔöÇ¿×éÖ¯ÐÅÏ¢µÄÃû³Æ [ 2 ] Nankai Univ, LPMC, Tianjin 300071, Peoples R China µç×ÓÓʼþµØÖ·:ww5998198@126.com; zqzhang@nankai.edu.cn »ù½ð×ÊÖúÖÂл »ù½ð×ÊÖú»ú¹¹ ÊÚȨºÅ National Natural Science Foundation of China (NNSF) 11271091 ²é¿´»ù½ð×ÊÖúÐÅÏ¢ ³ö°æÉÌ ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA Àà±ð / ·ÖÀà Ñо¿·½Ïò:Mathematics Web of Science Àà±ð:Mathematics ÎÄÏ×ÐÅÏ¢ ÎÄÏ×ÀàÐÍ:Article ÓïÖÖ:English Èë²ØºÅ: WOS:000343019800005 ISSN: 0022-1236 µç×Ó ISSN: 1096-0783 ÆäËûÐÅÏ¢ IDS ºÅ: AQ7SP Web of Science ºËÐĺϼ¯ÖÐµÄ "ÒýÓõIJο¼ÎÄÏ×": 22 Web of Science ºËÐĺϼ¯ÖÐµÄ "±»ÒýƵ´Î": 0 |
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