Communications in Partial Differential Equations · 2005 · 43 citations · 13 references
EngineeringMechanical EngineeringFinite Element AnalysisFinite Element MethodsInflammationBoundary ConditionsBoundary-value ProblemsPartial Differential EquationsElliptic Boundary-value ProblemsViscosityViscosity SolutionsWeak Boundary Conditions
ABSTRACT We obtain Alexandrov-Bakelman-Pucci type estimates for semicontinuous viscosity solutions of fully nonlinear elliptic inequalities in unbounded domains. Under suitable assumptions relating the geometry of the domain with structural conditions on the differential operator, we establish the validity of the weak maximum principle for solutions which are bounded from above. Two variants are also given, namely one for unbounded solutions in narrow domains and one for operators with possibly changing sign zero order coefficients in domains of small measure.
13