1,720,971 research outputs found
Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators.
No full textThe main scope of this article is to define the concept of principal eigenvalue for fully non linear second order operators in bounded domains that are elliptic, homogenous with lower order terms. In particular we prove maximum and comparison principle, Hölder and Lipschitz regularity. This leads to the existence of a first eigenvalue and eigenfunction and to the existence of solutions of Dirichlet problems within this class of operators
Uniqueness of the first eigenfunction for fully nonlinear equations: the radial case.
No full textThe concept of eigenvalue has recently been extended to a large class of fully-nonlinear operators, here for fully-nonlinear operators in non divergence form that present singularities and degeneracies similar to the p-Laplacian we prove that in the radial case the eigenfunction is simple
Boundary asymptotics of the ergodic functions associated with fully nonlinear operators through a liouville type theorem
Full text linkWe prove gradient boundary blow up rates for ergodic functions in bounded domains related to fully nonlinear degenerate/singular elliptic operators. As a consequence, we deduce the uniqueness, up to constants, of the ergodic functions. The results are obtained by means of a Liouville type classification theorem in half-spaces for infinite boundary value problems related to fully nonlinear, uniformly elliptic operators
Mixed boundary value problems for fully nonlinear degenerate or singular equations
No full textWe prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global Holder estimate for solutions, obtained by means of the comparison principle and the construction of ad hoc barriers. The global Holder estimate immediately yields a compactness result in the space of solutions, which could be applied in the study of principal eigenvalues and principal eigenfunctions of mixed boundary value problems. (c) 2022 Elsevier Ltd. All rights reserved
C1,γ regularity for singular or degenerate fully nonlinear equations and applications
Full text linkIn this note, we prove C1,γ regularity for solutions of some fully nonlinear degenerate elliptic equations with “superlinear” and “subquadratic” Hamiltonian terms. As an application, we complete the results of Birindelli et al. (ESAIM Control Optim Calc Var, 2019. https://doi.org/10.1051/cocv/2018070) concerning the associated ergodic problem, proving, among other facts, the uniqueness, up to constants, of the ergodic function
Dirichlet problems for fully nonlinear equations with “subquadratic” hamiltonians
No full textFor a class of fully nonlinear equations having second order operators which may be singular or degenerate when the gradient of the solutions vanishes, and having first order terms with power growth, we prove the existence and uniqueness of suitably defined viscosity solutions of Dirichlet problems and we further show that it is a Lipschitz continuous function
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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