Upper bounds for the eigenvalues of Hessian equations

We prove some upper bounds for the Dirichlet eigenvalues of a class of fully nonlinear elliptic equations, namely the Hessian equationsComment: 15 pages, 1 figur

Application of advanced computational procedures for modeling solar-wind interactions with Venus: Theory and computer code

Computational procedures are developed and applied to the prediction of solar wind interaction with nonmagnetic terrestrial planet atmospheres, with particular emphasis to Venus. The theoretical method is based on a single fluid, steady, dissipationless, magnetohydrodynamic continuum model, and is appropriate for the calculation of axisymmetric, supersonic, super-Alfvenic solar wind flow past terrestrial planets. The procedures, which consist of finite difference codes to determine the gasdynamic properties and a variety of special purpose codes to determine the frozen magnetic field, streamlines, contours, plots, etc. of the flow, are organized into one computational program. Theoretical results based upon these procedures are reported for a wide variety of solar wind conditions and ionopause obstacle shapes. Plasma and magnetic field comparisons in the ionosheath are also provided with actual spacecraft data obtained by the Pioneer Venus Orbiter

Computational techniques for solar wind flows past terrestrial planets: Theory and computer programs

The interaction of the solar wind with terrestrial planets can be predicted using a computer program based on a single fluid, steady, dissipationless, magnetohydrodynamic model to calculate the axisymmetric, supersonic, super-Alfvenic solar wind flow past both magnetic and nonmagnetic planets. The actual calculations are implemented by an assemblage of computer codes organized into one program. These include finite difference codes which determine the gas-dynamic solution, together with a variety of special purpose output codes for determining and automatically plotting both flow field and magnetic field results. Comparisons are made with previous results, and results are presented for a number of solar wind flows. The computational programs developed are documented and are presented in a general user's manual which is included

Monge's transport problem in the Heisenberg group

We prove the existence of solutions to Monge transport problem between two compactly supported Borel probability measures in the Heisenberg group equipped with its Carnot-Caratheodory distance assuming that the initial measure is absolutely continuous with respect to the Haar measure of the group

Local and global behaviour of nonlinear equations with natural growth terms

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results consist of optimal pointwise estimates for positive solutions of such equations in terms of two local Wolff's potentials.Comment: In memory of Professor Nigel Kalto

Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form

Coupling carbon allocation with leaf and root phenology predicts tree-grass partitioning along a savanna rainfall gradient

© Author(s) 2016. The relative complexity of the mechanisms underlying savanna ecosystem dynamics, in comparison to other biomes such as temperate and tropical forests, challenges the representation of such dynamics in ecosystem and Earth system models. A realistic representation of processes governing carbon allocation and phenology for the two defining elements of savanna vegetation (namely trees and grasses) may be a key to understanding variations in tree-grass partitioning in time and space across the savanna biome worldwide. Here we present a new approach for modelling coupled phenology and carbon allocation, applied to competing tree and grass plant functional types. The approach accounts for a temporal shift between assimilation and growth, mediated by a labile carbohydrate store. This is combined with a method to maximize long-term net primary production (NPP) by optimally partitioning plant growth between fine roots and (leaves + stem). The computational efficiency of the analytic method used here allows it to be uniquely and readily applied at regional scale, as required, for example, within the framework of a global biogeochemical model. We demonstrate the approach by encoding it in a new simple carbon-water cycle model that we call HAVANA (Hydrology and Vegetation-dynamics Algorithm for Northern Australia), coupled to the existing POP (Population Orders Physiology) model for tree demography and disturbance-mediated heterogeneity. HAVANA-POP is calibrated using monthly remotely sensed fraction of absorbed photosynthetically active radiation (fPAR) and eddy-covariance-based estimates of carbon and water fluxes at five tower sites along the North Australian Tropical Transect (NATT), which is characterized by large gradients in rainfall and wildfire disturbance. The calibrated model replicates observed gradients of fPAR, tree leaf area index, basal area, and foliage projective cover along the NATT. The model behaviour emerges from complex feedbacks between the plant physiology and vegetation dynamics, mediated by shifting above- versus below-ground resources, and not from imposed hypotheses about the controls on tree-grass co-existence. Results support the hypothesis that resource limitation is a stronger determinant of tree cover than disturbance in Australian savannas

Coupling carbon allocation with leaf and root phenology predicts tree-grass partitioning along a savanna rainfall gradient

Abstract. The relative complexity of the mechanisms underlying savanna ecosystem dynamics, in comparison to other biomes such as temperate and tropical forests, challenges the representation of such dynamics in ecosystem and Earth system models. A realistic representation of processes governing carbon allocation and phenology for the two defining elements of savanna vegetation (namely trees and grasses) may be a key to understanding variations in tree/grass partitioning in time and space across the savanna biome worldwide. Here we present a new approach for modelling coupled phenology and carbon allocation, applied to competing tree and grass plant functional types. The approach accounts for a temporal shift between assimilation and growth, mediated by a labile carbohydrate store. This is combined with a method to maximise long-term net primary production (NPP) by optimally partitioning plant growth between fine roots and (leaves + stem). The computational efficiency of the analytic method used here allows it to be uniquely and readily applied at regional scale, as required, for example, within the framework of a global biogeochemical model. We demonstrate the approach by encoding it in a new simple carbon/water cycle model that we call HAVANA (Hydrology and Vegetation-dynamics Algorithm for Northern Australia), coupled to the existing POP (Population Orders Physiology) model for tree demography and disturbance-mediated heterogeneity. HAVANA-POP is calibrated using monthly remotely-sensed fraction of absorbed photosynthetically active radiation (fPAR) and eddy-covariance-based estimates of carbon and water fluxes at 5 tower sites along the Northern Australian Tropical Transect (NATT), which is characterized by large gradients in rainfall and wildfire disturbance. The calibrated model replicates observed gradients of fPAR, tree leaf area index, basal area and foliage projective cover along the NATT. The model behaviour emerges from complex feed-backs between the plant physiology and vegetation dynamics, mediated by shifting above- vs. below-ground resources, and not from imposed hypotheses about the controls on tree/grass co-existence. Results support the hypothesis that resource limitation is a stronger determinant of tree cover than disturbance in Australian savannas. </jats:p

Existence and multiplicity for elliptic problems with quadratic growth in the gradient

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule.Comment: To appear in Comm. PD

Evolution models for mass transportation problems

We present a survey on several mass transportation problems, in which a given mass dynamically moves from an initial configuration to a final one. The approach we consider is the one introduced by Benamou and Brenier in [5], where a suitable cost functional $F(\rho,v)$, depending on the density $\rho$ and on the velocity $v$ (which fulfill the continuity equation), has to be minimized. Acting on the functional $F$ various forms of mass transportation problems can be modeled, as for instance those presenting congestion effects, occurring in traffic simulations and in crowd motions, or concentration effects, which give rise to branched structures.Comment: 16 pages, 14 figures; Milan J. Math., (2012