A Variational Inequality for a Degenerate Elliptic Operator Under Minimal Assumptions on the Coefficients

Carmela Vitanza; Pietro Zamboni

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 2, page 341-356
  • ISSN: 0392-4041

Abstract

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In this note we obtain the existence and the uniqueness of the solution of a variational inequality associated to the degenerate operator L ⁢ u = - ∑ i , j = 1 n ( a i ⁢ j ⁢ ( x ) ⁢ u x i + d j ⁢ u ) x j + ∑ i = 1 n b i ⁢ u x i + c ⁢ u assuming the coefficients of the lower terms and the known term belonging to a suitable degenerate Stummel-Kato class. The weight w , which gives the degeneration, belongs to the Muckenoupt class A 2 .

How to cite

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Vitanza, Carmela, and Zamboni, Pietro. "A Variational Inequality for a Degenerate Elliptic Operator Under Minimal Assumptions on the Coefficients." Bollettino dell'Unione Matematica Italiana 10-B.2 (2007): 341-356. <http://eudml.org/doc/290422>.

@article{Vitanza2007,
abstract = {In this note we obtain the existence and the uniqueness of the solution of a variational inequality associated to the degenerate operator \begin\{equation*\}\tag\{*\} Lu = - \sum^n\_\{i,j=1\} (a\_\{ij\}(x)u\_\{x\_i\} + d\_j u)\_\{x\_j\} + \sum^n\_\{i=1\} b\_i u\_\{x\_i\} + cu\end\{equation*\} assuming the coefficients of the lower terms and the known term belonging to a suitable degenerate Stummel-Kato class. The weight $w$, which gives the degeneration, belongs to the Muckenoupt class $A^2$.},
author = {Vitanza, Carmela, Zamboni, Pietro},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {341-356},
publisher = {Unione Matematica Italiana},
title = {A Variational Inequality for a Degenerate Elliptic Operator Under Minimal Assumptions on the Coefficients},
url = {http://eudml.org/doc/290422},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Vitanza, Carmela
AU - Zamboni, Pietro
TI - A Variational Inequality for a Degenerate Elliptic Operator Under Minimal Assumptions on the Coefficients
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/6//
PB - Unione Matematica Italiana
VL - 10-B
IS - 2
SP - 341
EP - 356
AB - In this note we obtain the existence and the uniqueness of the solution of a variational inequality associated to the degenerate operator \begin{equation*}\tag{*} Lu = - \sum^n_{i,j=1} (a_{ij}(x)u_{x_i} + d_j u)_{x_j} + \sum^n_{i=1} b_i u_{x_i} + cu\end{equation*} assuming the coefficients of the lower terms and the known term belonging to a suitable degenerate Stummel-Kato class. The weight $w$, which gives the degeneration, belongs to the Muckenoupt class $A^2$.
LA - eng
UR - http://eudml.org/doc/290422
ER -

References

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