Generalized Derivatives for the Solution Operator of the Obstacle Problem
Sign Up to like & getrecommendations! Published in 2019 at "Set-Valued and Variational Analysis"
DOI: 10.1007/s11228-019-0506-y
Abstract: We characterize generalized derivatives of the solution operator of the obstacle problem. This precise characterization requires the usage of the theory of so-called capacitary measures and the associated solution operators of relaxed Dirichlet problems. The… read more here.
Keywords: derivatives solution; obstacle problem; generalized derivatives;
On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125895
Abstract: The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings… read more here.
Keywords: local analysis; contained graphs; subspaces contained; analysis multifunctions ... See more keywords
Computationally relevant generalized derivatives: theory, evaluation and applications
Sign Up to like & getrecommendations! Published in 2018 at "Optimization Methods and Software"
DOI: 10.1080/10556788.2017.1374385
Abstract: A new method for evaluating generalized derivatives in nonsmooth problems is reviewed. Lexicographic directional (LD-)derivatives are a recently developed tool in nonsmooth analysis for evaluating generalized derivative elements in a tractable and robust way. Applicable… read more here.
Keywords: computationally relevant; derivatives theory; generalized derivatives; theory evaluation ... See more keywords
Generalized Derivatives for Hybrid Systems
Sign Up to like & getrecommendations! Published in 2017 at "IEEE Transactions on Automatic Control"
DOI: 10.1109/tac.2016.2644759
Abstract: Established sensitivity results for hybrid discrete/continuous dynamic systems are generalized by relaxing smoothness assumptions on the functions governing the systems' continuous evolution and discrete event handling. The new results only require L-smoothness of these functions… read more here.
Keywords: derivatives hybrid; hybrid systems; generalized derivatives; sensitivity ... See more keywords
On Continuity of Functions With Generalized Derivatives
Sign Up to like & getrecommendations! Published in 2018 at "Russian Mathematics"
DOI: 10.3103/s1066369x18110087
Abstract: We study the question of the continuity of functions for which the generalized gradient belongs to the Lorentz spaces. read more here.
Keywords: continuity functions; functions generalized; generalized derivatives;
New Analytical Solutions for Coupled Stochastic Korteweg-de Vries Equations via Generalized Derivatives
Sign Up to like & getrecommendations! Published in 2022 at "Symmetry"
DOI: 10.3390/sym14091770
Abstract: In this paper, the coupled nonlinear KdV (CNKdV) equations are solved in a stochastic environment. Hermite transforms, generalized conformable derivative, and an algorithm that merges the white noise instruments and the (G′/G2)-expansion technique are utilized… read more here.
Keywords: stochastic korteweg; generalized derivatives; coupled stochastic; solutions coupled ... See more keywords