Schwarz problem for higher‐order complex partial differential equations in the upper half plane

Aksoy ümit; Begehr Heinrich; ?elebi A. Okay

摘要

Abstract >Linear and nonlinear elliptic complex partial differential equations of higher‐order are considered under Schwarz conditions in the upper‐half plane. Firstly, using the integral representations for the solutions of the inhomogeneous polyanalytic equation with Schwarz conditions, a class of integral operators is introduced together with some of their properties. Then, these operators are used to transform the problem for linear equations into singular integral equations. In the case of nonlinear equations such a transformation yields a system of integro‐differential equations. Existence of the solutions of the relevant boundary value problems for linear and nonlinear equations are discussed via Fredholm theory and fixed point theorems, respectively. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”> <标题类型=“main”>抽象</ title> >在上半平面中的施瓦茨条件下考虑高阶的线性和非线性椭圆形复杂部分微分方程。首先，利用与施瓦茨条件的非均匀多分析式方程解的整体表示，一类整体运算符与其中一些属性一起引入。然后，这些运营商用于将线性方程的问题转换为奇异积分方程。在非线性方程的情况下，这种变换产生积分微分方程的系统。通过Fredholm理论和定理定理分别讨论了线性和非线性方程相关边值问题的解决方案的存在。</ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-24615/'>《Mathematische Nachrichten》</a> <b style="margin: 0 2px;">|</b><span>2019年第6期</span><b style="margin: 0 2px;">|</b><span>共11页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Aksoy ümit&option=202" target="_blank" rel="nofollow">Aksoy ümit;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Begehr Heinrich&option=202" target="_blank" rel="nofollow">Begehr Heinrich;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=?elebi A. Okay&option=202" target="_blank" rel="nofollow">?elebi A. Okay;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of MathematicsAtilim UniversityAnkara Turkey;</p> <p>Institut für MathematikFreie Universit?t BerlinArnimallee 2–6 14195 Berlin Germany;</p> <p>Department of MathematicsYeditepe University?stanbul Turkey;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/156.html" title="数学">数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=complex partial differential equation&option=203" rel="nofollow">complex partial differential equation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=polyanalytic&option=203" rel="nofollow">polyanalytic;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Schwarz problem&option=203" rel="nofollow">Schwarz problem;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=upper half plane&option=203" rel="nofollow">upper half plane;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=30E25&option=203" rel="nofollow">30E25;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=30G20&option=203" rel="nofollow">30G20;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=35G15&option=203" rel="nofollow">35G15;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=35G30&option=203" rel="nofollow">35G30;</a> </p> <div class="translation"> 机译：复杂的部分微分方程;多分析性;施瓦茨问题;上半平面;30E25;30G20;35G15;35G30; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704023595755.html">Schwarz problem for higher‐order complex partial differential equations in the upper half plane</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Aksoy ümit&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Aksoy ümit,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Begehr Heinrich&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Begehr Heinrich,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=?elebi A. 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rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 杨柳</a> <span> . 2005</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/061201174082.html">生成可缩放矢量图形场景的至少一部分的复杂度矢量的方法和设备以及用于测试可缩放矢量图形场景的至少一部分在设备上的播放适宜性的方法和测试设备</a> <b>[P]</b> . <span> 中国专利： CN101689208B </span> <span> . 2013.05.01</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06120105904048.html">生成可缩放矢量图形场景的至少一部分的复杂度矢量的方法和设备以及用于测试可缩放矢量图形场景的至少一部分在设备上的播放适宜性的方法和测试设备</a> <b>[P]</b> . <span> 中国专利： CN101689208A </span> <span> . 2010-03-31</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130444736589.html">Program generation method for calculation of a Poisson equation, diffusion equation, or like partial differential equation performed on irregularly dispersed grid points</a> <b>[P]</b> . <span> 外国专利：  US6574650B1 </span> <span> . 2003-06-03</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：用于对不规则分散的网格点执行的泊松方程，扩散方程或类似偏微分方程的计算的程序生成方法 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130451247807.html">HIGHLY ACCURATE CALCULATION PROGRAM FOR POISSON EQUATION DIFFUSION EQUATION AND SIMILAR PARTIAL DIFFERENTIATION EQUATION USING SPATIAL DIFFERENTIAL COEFFICIENT IN NON-EQUAL INTERVAL GRATING</a> <b>[P]</b> . <span> 外国专利：  JP2000293508A </span> <span> . 2000-10-20</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：非均值区间划分中使用空间微分系数的Poisson方程扩散方程和类似的偏微分方程的高精度计算程序 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130500728137.html">MACHINE-LEARNING BASED SOLVER OF COUPLED-PARTIAL DIFFERENTIAL EQUATIONS</a> <b>[P]</b> . <span> 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