scholarly journals Regularity Theory for Rough Partial Differential Equations and Parabolic Comparison Revisited

2014 ◽  
pp. 203-238 ◽  
Author(s):  
Joscha Diehl ◽  
Peter K. Friz ◽  
Harald Oberhauser
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Regularity Theory ◽  
Partial Differential

scholarly journals Regularity theory in Colombeau algebras

2006 ◽  
Vol 133 (31) ◽  
pp. 147-162 ◽  
Author(s):  
M. Oberguggenberger
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Equations ◽  
Regularity Theory ◽  
Subject Classification ◽  
Regularity Of Solutions ◽  
Partial Differential ◽  
Delta Waves ◽  
Colombeau Algebras

This paper introduces and discusses various notions of regularity of solutions to partial differential equations in Colombeau algebras. The aim is to suggest a number of approaches that allow to extend the regularity theory to nonlinear equations. A relation with the notion of delta waves is observed. AMS Mathematics Subject Classification (2000): 35D05, 35L60, 46F30.

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