A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight

Abstract

Abstract This paper gives a Caccioppoli-type estimate for very weak solutions to obstacle problems of the A -harmonic equation div A ( x , ∇ u ) = 0 with | A ( x , ξ ) | ≈ w ( x ) | ξ | p - 1 , where 1 < p < ∞ and w(x) be a Muckenhoupt A1 weight. Mathematics Subject Classification (2000) 35J50, 35J60

Keywords

• Caccioppoli-type estimate
• very weak solution
• obstacle problem
• Mucken-houpt weight
• A -harmonic equation%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <inline-formula><m:math name="1029-242X-2011-58-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="script">A</m:mi> </m:math> </inline-formula>-harmonic equation