On the local boundedness of maximal H-monotone operators

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• 作者：Z.M. Balogh^a ; ^{zoltan.balogh@math.unibe.ch" class="auth_mail" title="E-mail the corresponding author} ; A. Calogero^b ; ^{andrea.calogero@unimib.it" class="auth_mail" title="E-mail the corresponding author} ; R. Pini^b ; ^{rita.pini@unimib.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：47H05 ; 49J53
• 刊名：Nonlinear Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：148
• 期：Complete
• 页码：88-105
• 全文大小：693 K

文摘

In this paper we prove that maximal H-monotone operators mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302371&_mathId=si1.gif&_user=111111111&_pii=S0362546X16302371&_rdoc=1&_issn=0362546X&md5=a321c42f468ea972515c31bfa7818aa2" title="Click to view the MathML source">T:Hⁿ⇉V₁mathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mi>Tmi><mo>:mo><msup><mrow><mi mathvariant="double-struck">Hmi>mrow><mrow><mi>nmi>mrow>msup><mo>⇉mo><msub><mrow><mi>Vmi>mrow><mrow><mn>1mn>mrow>msub>math> whose domain is all the Heisenberg group mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302371&_mathId=si2.gif&_user=111111111&_pii=S0362546X16302371&_rdoc=1&_issn=0362546X&md5=e72ca78a98fd5252861c18df0710b991" title="Click to view the MathML source">HⁿmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><msup><mrow><mi mathvariant="double-struck">Hmi>mrow><mrow><mi>nmi>mrow>msup>math> are locally bounded. This implies that they are upper semicontinuous. As a consequence, maximal H-monotonicity of an operator on mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302371&_mathId=si2.gif&_user=111111111&_pii=S0362546X16302371&_rdoc=1&_issn=0362546X&md5=e72ca78a98fd5252861c18df0710b991" title="Click to view the MathML source">HⁿmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><msup><mrow><mi mathvariant="double-struck">Hmi>mrow><mrow><mi>nmi>mrow>msup>math> can be characterized by a suitable version of Minty’s type theorem.