1,721,017 research outputs found
Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues
Full text linkWe consider the Dirichlet problem for partial trace operators which include the smallest and the largest eigenvalue of the Hessian matrix. It is related to two-player zero-sum differential games. No Lipschitz regularity result is known for the solutions, to our knowledge. If some eigenvalue is missing, such operators are nonlinear, degenerate, non-uniformly elliptic, neither convex nor concave. Here we prove an interior Lipschitz estimate under a non-standard assumption: that the solution exists in a larger, unbounded domain, and vanishes at infinity. In other words, we need a condition coming from far away. We also provide existence results showing that this condition is satisfied for a large class of solutions. On the occasion, we also extend a few qualitative properties of solutions, known for uniformly elliptic operators, to partial trace operators
Phragmèn-Lindelöf principles for nonlinear elliptic equations
No full textThis paper contains Phragmèn-Lindelöf type results for viscosity solutions of fully nonlinear second-order uniformly elliptic equations with superlinear gradient term in a wide class of unbounded domains. Under suitable assumptions on the coefficients, as classically, we show that the Maximum Principle holds in a generalized version of cylindrical and conical domains, resp., for subsolutions with exponential and polynomial growth at infinit
Generalized Keller–Osserman Conditions for Fully Nonlinear Degenerate Elliptic Equations
Full text linkWe discuss the existence of entire (i.e. defined on the whole space) subsolutions of fully nonlinear degenerate elliptic equations, giving necessary and sufficient conditions on the coefficients of the lower order terms which extend the classical Keller–Osserman conditions for semilinear elliptic equations. Our analysis shows that, when the conditions of existence of entire subsolutions fail, a priori upper bounds for local subsolutions can be obtained
Imbedding estimates and elliptic equations with discontinuous coefficients in unbounded domains
No full textIn this paper we deal with the multiplication operator u ∈ W^{k,p} (Ω) → gu ∈ L^q (Ω), with g belonging to a space of Morrey type. We apply our results in order to establish an a-priori bound for the solutions of the Dirichlet problem concerning elliptic equations with discontinuous coefficients
Imbedding estimates and elliptic equations with discontinuous coefficients in unbounded domains
Full text linkIn this paper we deal with the multiplication operator u ∈ W^{k,p} (Ω) → gu ∈ L^q (Ω), with g belonging to a space of Morrey type. We apply our results in order to establish an a-priori bound for the solutions of the Dirichlet problem concerning elliptic equations with discontinuous coefficients
Optimization of the energy integral in two classes of rearrangements
No full textThis paper concerns the maximization and the minimization of the energy
integral associated to a second order elliptic problem in classes of rearrangements with respect to either the Lebesgue measure or to a measure related to
the structure of the equation. We find results of existence, uniqueness and representation of the maximizers and the minimizers. Precise characterizations
of the optimizers are found in case the domain is a ball. Finally, the effect of
special geometrical transformations concerning these problems is discussed
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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