Isogroups of differential ideals of vector-valued differential forms: Application to partial differential equations

1988 ◽  
Vol 11 (2) ◽  
pp. 155-175 ◽  
Author(s):  
C. J. Papachristou ◽  
B. Kent Harrison
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Differential Forms ◽  
Partial Differential ◽  
Vector Valued

Learning sparse partial differential equations for vector-valued images

2016 ◽  
Vol 29 (11) ◽  
pp. 1205-1216 ◽  
Author(s):  
Yuanyuan Jiao ◽  
Xiaogang Pan ◽  
Zhenyu Zhao ◽  
Chenping Hou
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Vector Valued

scholarly journals Embedding of vector-valued Morrey spaces and separable differential operators

2019 ◽  
Vol 09 (02) ◽  
pp. 1950013 ◽  
Author(s):  
Maria Alessandra Ragusa ◽  
Veli Shakhmurov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Differential Operators ◽  
Maximal Regularity ◽  
Elliptic Partial Differential Equations ◽  
Morrey Spaces ◽  
Embedding Theorems ◽  
Partial Differential ◽  
Infinite Systems ◽  
Vector Valued

The paper is the first part of a program devoted to the study of the behavior of operator-valued multipliers in Morrey spaces. Embedding theorems and uniform separability properties involving [Formula: see text]-valued Morrey spaces are proved. As a consequence, maximal regularity for solutions of infinite systems of anisotropic elliptic partial differential equations are established.

Vector-Valued Partial Differential Equations and Applications

2017 ◽  
Author(s):  
Bernard Dacorogna ◽  
Nicola Fusco ◽  
Stefan Müller ◽  
Vladimir Sverak
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Vector Valued

scholarly journals Reduced dimensional Gaussian process emulators of parametrized partial differential equations based on Isomap

2015 ◽  
Vol 471 (2174) ◽  
pp. 20140697 ◽  
Author(s):  
Wei Xing ◽  
Akeel A. Shah ◽  
Prasanth B. Nair
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dimensionality Reduction ◽  
Gaussian Process ◽  
Response Surfaces ◽  
Nonlinear Dimensionality Reduction ◽  
Partial Differential ◽  
Parametrized Partial Differential Equations ◽  
Vector Valued ◽  
Output Space

In this paper, Isomap and kernel Isomap are used to dramatically reduce the dimensionality of the output space to efficiently construct a Gaussian process emulator of parametrized partial differential equations. The output space consists of spatial or spatio-temporal fields that are functions of multiple input variables. For such problems, standard multi-output Gaussian process emulation strategies are computationally impractical and/or make restrictive assumptions regarding the correlation structure. The method we develop can be applied without modification to any problem involving vector-valued targets and vector-valued inputs. It also extends a method based on linear dimensionality reduction to response surfaces that cannot be described accurately by a linear subspace of the high dimensional output space. Comparisons to the linear method are made through examples that clearly demonstrate the advantages of nonlinear dimensionality reduction.

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