Dirichlet problems with fractional competing operators and fractional convection
Laura Gambera, S. Marano, Dumitru Motreanu
Abstract
Abstract In this paper, the existence of weak solutions to some Dirichlet problems with fractional competing operators and distributional Riesz fractional gradient is investigated. Due to the nature of driving operators, the most known techniques, basically based on ellipticity and monotonicity, are no longer applicable. Generalized solutions (in a suitable sense) are obtained via an approximation procedure and a corollary of the Brouwer fixed point theorem.
Topics & Concepts
MathematicsCorollaryMonotonic functionDirichlet distributionFractional calculusFixed-point theoremApplied mathematicsMathematical analysisPure mathematicsBoundary value problemNonlinear Partial Differential EquationsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems