scholarly journals Approximations of Very Weak Solutions to Boundary-Value Problems

2004 ◽  
Vol 42 (2) ◽  
pp. 860-877 ◽  
Author(s):  
Martin Berggren
Keyword(s):  
Boundary Value Problems ◽  
Weak Solutions ◽  
Boundary Value ◽  
Very Weak Solutions

scholarly journals Integrability of Very Weak Solutions for Boundary Value Problems of Nonhomogeneous p-Harmonic Equations

2019 ◽  
pp. 1-9
Author(s):  
Yeqing Zhu ◽  
Yanxia Zhou ◽  
Yuxia Tong
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Weak Solutions ◽  
Boundary Value ◽  
Very Weak Solutions ◽  
Very Weak Solution ◽  
Harmonic Equation

The paper deals with very weak solutions u to boundary value problems of the nonhomogeneous p-harmonic equation. We show that, any very weak solution u to the boundary value problem is integrable provided that r is sufficiently close to p.

Very weak solutions of boundary value problems for the Laplace operator and the Lamé system on polyhedral domains in ℝ3

1994 ◽  
Vol 124 (4) ◽  
pp. 645-672
Author(s):  
Ding Hua
Keyword(s):  
Boundary Value Problems ◽  
Laplace Operator ◽  
Weak Solutions ◽  
Boundary Value ◽  
Very Weak Solutions ◽  
Nonsmooth Data ◽  
Lamé System ◽  
Variational Solutions ◽  
Lame System ◽  
The Laplace Operator

The notion of very weak solutions is introduced in this paper in order to solve the boundary value problems for the Laplace operator and for the Lamé system with nonsmooth data in polyhedral domains. A continuity theorem is given for variational solutions of the above problems. This result may be used to solve problems with concentrated loads.

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