Flux in axiomatic potential theory. II. Duality

@article{Walsh1969,
abstract = {This is a continuation of an earlier paper [Inventiones Math., 8 (1969), 175-221]. It is assumed that a space $W$ and a sheaf $\{\bf H\}$ over $W$ are given, such that the pair $(W,\{\bf H\})$ satisfies the Brelot axioms and also satisfies, locally, the additional hypotheses of the theory of adjoint sheaves. The following subjects are considered: 1) Extension of the adjoint-sheaf theory to the case where $(W,\{\bf H\})$ does not admit a global potential (in particular, the case where $W$ is compact). 2) Construction of a new fine resolution $O\rightarrow \{\bf H\}\rightarrow \{\bf R\}\rightarrow \{\bf L\}\rightarrow O$ of the sheaf $\{\bf H\}$, in which $\{\bf L\}$ is a (complete pre-)sheaf of measures on $W$. 3) Construction of a natural duality between the flux functional corresponds to a distinguished positive element of $H^*_W$.},
author = {Walsh, Bertram},
journal = {Annales de l'institut Fourier},
keywords = {partial differential equations},
language = {eng},
number = {2},
pages = {371-417},
publisher = {Association des Annales de l'Institut Fourier},
title = {Flux in axiomatic potential theory. II. Duality},
url = {http://eudml.org/doc/73995},
volume = {19},
year = {1969},
}

TY - JOUR
AU - Walsh, Bertram
TI - Flux in axiomatic potential theory. II. Duality
JO - Annales de l'institut Fourier
PY - 1969
PB - Association des Annales de l'Institut Fourier
VL - 19
IS - 2
SP - 371
EP - 417
AB - This is a continuation of an earlier paper [Inventiones Math., 8 (1969), 175-221]. It is assumed that a space $W$ and a sheaf ${\bf H}$ over $W$ are given, such that the pair $(W,{\bf H})$ satisfies the Brelot axioms and also satisfies, locally, the additional hypotheses of the theory of adjoint sheaves. The following subjects are considered: 1) Extension of the adjoint-sheaf theory to the case where $(W,{\bf H})$ does not admit a global potential (in particular, the case where $W$ is compact). 2) Construction of a new fine resolution $O\rightarrow {\bf H}\rightarrow {\bf R}\rightarrow {\bf L}\rightarrow O$ of the sheaf ${\bf H}$, in which ${\bf L}$ is a (complete pre-)sheaf of measures on $W$. 3) Construction of a natural duality between the flux functional corresponds to a distinguished positive element of $H^*_W$.
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/73995
ER -