scholarly journals Solving Variational Problems and Partial Differential Equations Mapping into General Target Manifolds

2002 ◽  
Author(s):  
Facundo Memoli ◽  
Guillermo Sapiro ◽  
Stanley Osher
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Variational Problems ◽  
Partial Differential

Variational Problems and Partial Differential Equations on Implicit Surfaces

2001 ◽  
Vol 174 (2) ◽  
pp. 759-780 ◽  
Author(s):  
Marcelo Bertalmı́o ◽  
Li-Tien Cheng ◽  
Stanley Osher ◽  
Guillermo Sapiro
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Variational Problems ◽  
Implicit Surfaces ◽  
Partial Differential

scholarly journals On a new class of fractional partial differential equations

2015 ◽  
Vol 8 (4) ◽  
Author(s):  
Tien-Tsan Shieh ◽  
Daniel E. Spector
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Variational Problems ◽  
Fractional Sobolev Spaces ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
New Class ◽  
Natural Way

AbstractIn this paper, we study a new class of fractional partial differential equations which are obtained by minimizing variational problems in fractional Sobolev spaces. We introduce a notion of fractional gradient which has the potential to extend many classical results in the Sobolev spaces to the nonlocal and fractional setting in a natural way.

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