Degenerate Elliptic Equations and Morrey Spaces

Francesco Borrello

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 989-1011
  • ISSN: 0392-4041

Abstract

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In this paper we study local regularity for the generalized solution to the Dirichlet problem related to the equation L ⁢ u ≡ X i * ⁢ ( a i ⁢ j ⁢ X j ⁢ u ) = f . where X 1 , X 2 , … , X m are vector fields satisfying Hörmander condition and a i ⁢ j ∈ L ∞ . We give a representation formula for the generalized solution in terms of the Green function and thanks to suitable estimates we achieve our goal. In the case f ≥ 0 we are able to give necessary condition too.

How to cite

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Borrello, Francesco. "Degenerate Elliptic Equations and Morrey Spaces." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 989-1011. <http://eudml.org/doc/290421>.

@article{Borrello2007,
abstract = {In this paper we study local regularity for the generalized solution to the Dirichlet problem related to the equation \begin\{equation*\} Lu \equiv X^*\_i (a\_\{ij\}X\_ju)=f. \end\{equation*\} where $X_\{1\}, X_2, \ldots, X_m$ are vector fields satisfying Hörmander condition and $a_\{ij\}\in L^\infty$. We give a representation formula for the generalized solution in terms of the Green function and thanks to suitable estimates we achieve our goal. In the case $f \geq 0$ we are able to give necessary condition too.},
author = {Borrello, Francesco},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {989-1011},
publisher = {Unione Matematica Italiana},
title = {Degenerate Elliptic Equations and Morrey Spaces},
url = {http://eudml.org/doc/290421},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Borrello, Francesco
TI - Degenerate Elliptic Equations and Morrey Spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 989
EP - 1011
AB - In this paper we study local regularity for the generalized solution to the Dirichlet problem related to the equation \begin{equation*} Lu \equiv X^*_i (a_{ij}X_ju)=f. \end{equation*} where $X_{1}, X_2, \ldots, X_m$ are vector fields satisfying Hörmander condition and $a_{ij}\in L^\infty$. We give a representation formula for the generalized solution in terms of the Green function and thanks to suitable estimates we achieve our goal. In the case $f \geq 0$ we are able to give necessary condition too.
LA - eng
UR - http://eudml.org/doc/290421
ER -

References

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