On Besov regularity of solutions to nonlinear elliptic partial differential equations

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• 作者：Stephan Dahlke (1)
  Winfried Sickel (2)
  
• 关键词：(Nonlinear) elliptic equation ; Regularity of solutions ; Besov spaces ; Linear and nonlinear approximation methods ; 41A25 ; 41A46 ; 41A65 ; 42C40 ; 65C99
• 刊名：Revista Matem篓垄tica Complutense
• 出版年：2013
• 出版时间：January 2013
• 年：2013
• 卷：26
• 期：1
• 页码：115-145
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• 作者单位：Stephan Dahlke (1)
  Winfried Sickel (2)
  
  1. FB12 Mathematik und Informatik, Philipps-Universit盲t Marburg, Hans-Meerwein Stra脽e, Lahnberge, 35032, Marburg, Germany
  2. Mathematisches Institut, Friedrich-Schiller-Universit盲t Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany
  
• ISSN：1988-2807

文摘

In this paper, we study the regularity of the solutions to nonlinear elliptic equations. In particular, we are interested in smoothness estimates in the specific scale $B^{\alpha}_{\tau}(L_{\tau})$ , 蟿=(伪/d+1/2)鈭?, of Besov spaces which determines the approximation order of adaptive and other nonlinear numerical approximation schemes with respect to the L 2-norm. We show that the Besov regularity is high enough to justify the use of adaptive schemes.