Zeitschrift für Analysis und ihre Anwendungen · 2009 · 134 citations · 6 references
Natural SciencesMathematics EducationComputational Fluid DynamicsFinite Element AnalysisFluid DynamicsBoundary ConditionsBoundary-value ProblemsPartial Differential EquationsElliptic Boundary-value ProblemsElliptic Partial Differential EquationsExistence ConditionsStrong SolutionsViscosityViscosity SolutionsWeak Boundary Conditions
In this paper we extend Caffarelli's result on interior W^{2,p} -estimates for viscosity solutions of uniformly elliptic equations and prove W^{2,p} -estimates at a flat boundary. Moreover we extend a result of A. Świech and prove W^{1,p} -estimates at the boundary. Thereafter we combine these results and prove global W^{2,p} -estimates for equations with dependence on Du and u . Finally, we show that the previous estimates lead to an existence result for W^{2,p} -strong solutions.
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