A strong harmonic representation theorem on complex spaces with isolated singularities

1991 ◽  
pp. 170-176
Author(s):  
Takeo Ohsawa
Keyword(s):  
Representation Theorem ◽  
Isolated Singularities ◽  
Complex Spaces ◽  
Harmonic Representation

Time-isolated Singularities of Temperatures

1998 ◽  
Vol 65 (3) ◽  
pp. 416-429
Author(s):  
Neil A. Watson
Keyword(s):  
Heat Equation ◽  
Compact Subset ◽  
Representation Theorem ◽  
Decomposition Theorem ◽  
Isolated Singularities ◽  
Open Set

AbstractWe study singularities of solutions of the heat equation, that are not necessarily isolated but occur only in a single characteristic hyperplane. We prove a decomposition theorem for certain solutions on D+ = D ∩ (Rn × ]0. ∞[), for a suitable open set D, with singularities at compact subset K of Rn × {0}, in terms of Gauss-Weierstrass integrals. We use this to prove a representation theorem for certain solutions on D+, with singularities at K, as the sums of potentials and Dirichlet solutions. We also give conditions under which K is removable for solutions on D∖K.

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