Caccioppoli estimates and very weak solutions of elliptic equations
Tadeusz Iwaniec; Carlo Sbordone
- Volume: 14, Issue: 3, page 189-205
- ISSN: 1120-6330
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topIwaniec, Tadeusz, and Sbordone, Carlo. "Caccioppoli estimates and very weak solutions of elliptic equations." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 14.3 (2003): 189-205. <http://eudml.org/doc/252298>.
@article{Iwaniec2003,
abstract = {Caccioppoli estimates are instrumental in virtually all analytic aspects of the theory of partial differential equations, linear and nonlinear. And there is always something new to add to these estimates. We emphasize the fundamental role of the natural domain of definition of a given differential operator and the associated weak solutions. However, we depart from this usual setting (energy estimates) and move into the realm of the so-called very weak solutions where important new applications lie. We carry out this task deliberately with a restricted generality in interest of readability, and we hope it pays off handsomely in mathematical insights.},
author = {Iwaniec, Tadeusz, Sbordone, Carlo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Caccioppoli inequality; Very weak solutions; Elliptic equations; very weak solutions; elliptic equations},
language = {eng},
month = {9},
number = {3},
pages = {189-205},
publisher = {Accademia Nazionale dei Lincei},
title = {Caccioppoli estimates and very weak solutions of elliptic equations},
url = {http://eudml.org/doc/252298},
volume = {14},
year = {2003},
}
TY - JOUR
AU - Iwaniec, Tadeusz
AU - Sbordone, Carlo
TI - Caccioppoli estimates and very weak solutions of elliptic equations
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/9//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 3
SP - 189
EP - 205
AB - Caccioppoli estimates are instrumental in virtually all analytic aspects of the theory of partial differential equations, linear and nonlinear. And there is always something new to add to these estimates. We emphasize the fundamental role of the natural domain of definition of a given differential operator and the associated weak solutions. However, we depart from this usual setting (energy estimates) and move into the realm of the so-called very weak solutions where important new applications lie. We carry out this task deliberately with a restricted generality in interest of readability, and we hope it pays off handsomely in mathematical insights.
LA - eng
KW - Caccioppoli inequality; Very weak solutions; Elliptic equations; very weak solutions; elliptic equations
UR - http://eudml.org/doc/252298
ER -
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