Search results for "solution"
showing 10 items of 5638 documents
Hölder gradient regularity for the inhomogeneous normalized p(x)-Laplace equation
2022
We prove the local gradient Hölder regularity of viscosity solutions to the inhomogeneous normalized p(x)-Laplace equation −Δp(x)Nu=f(x), where p is Lipschitz continuous, infp>1, and f is continuous and bounded. peerReviewed
Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian
2018
In this paper, we study an evolution equation involving the normalized [Formula: see text]-Laplacian and a bounded continuous source term. The normalized [Formula: see text]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [Formula: see text] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.
Regularity for nonlinear stochastic games
2015
We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed
Remarks on regularity for p-Laplacian type equations in non-divergence form
2018
We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.
Lidar detection of carbon dioxide in volcanic plumes
2015
Volcanic gases give information on magmatic processes. In particular, anomalous releases of carbon dioxide precede volcanic eruptions. Up to now, this gas has been measured in volcanic plumes with conventional measurements that imply the severe risks of local sampling and can last many hours. For these reasons and for the great advantages of laser sensing, the thorough development of volcanic lidar has been undertaken at the Diagnostics and Metrology Laboratory (UTAPRAD-DIM) of the Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA). In fact, lidar profiling allows one to scan remotely volcanic plumes in a fast and continuous way, and with high s…
Volumes of aqueous block copolymers based on poly(propylene oxides) and poly(ethylene oxides) in a large temperature range: A quantitative description
2006
The focus of this paper was on a quantitative comprehension of temperature effect on the volumes of aqueous di-block and triblock copolymers, based on propylene oxide (PO) and ethylene oxide (EO) units. To this purpose, literature data dealing with (EO316PO94 + water) and (EO13PO30EO13 + water) mixtures were analyzed. The volume vs. temperature trends were rationalized on the basis of the (unimers + aggregate) equilibrium by taking into account the temperature effect on both the partial molar volumes of the unimeric and the aggregated copolymer as well as the equilibrium constant of micellization. The analysis extended to the expansibility allowed to quantify the contribution for the shift …
Chemical weathering of volcanic rocks, Pantelleria Island: information from soil profile and soil solution investigations
2007
Concentrations of major, minor and trace elements were determined in soil profiles and soil solutions from the island of Pantelleria, Sicily Channel, to evaluate the weathering extent of soils evolved on trachytic and pantelleritic rocks and the aqueous transport of elements by their soil solutions. The chemical index of alteration (CIA) indicates a low-to-moderate degree of weathering; consistently, the mineralogical and geochemical imprints of the parent rocks are generally preserved. The chemical weathering appears to be incongruent, owing to primary minerals and glass dissolving to a variable degree while secondary minerals have formed. Based on the calculated saturation state of primar…
HIGH-RESOLUTION SEISMIC SURVEY IN THE WESTERN CALABRIA AND EASTERN SICILY OFFSHORE: IMPLICATIONS WITH VERTICAL TECTONICS
2016
High-resolution seismic data acquired along the continental shelf/upper slope offshore of Capo Vaticano (western Calabria), Milazzo Promontory and Mt. Etna (eastern Sicily) allow to provide new insights on vertical mobility related to active tectonics. A number of depositional sequences bounded by unconformities or correlative para-conformities were recognized on Sparker profiles in the first 200-300 m below the sea-floor. The most recent sequence overlays a widespread erosional surface that ostensibly formed during the sea level stillstand of the Last Glacial Maximum (LGM), whereas a stack of depositional sequences, which are interpreted as representing the falling and low-stand systems tr…
Recognizing Video Resolution by Monitoring Memory Metrics in Mobile Clients
2019
Content delivery is one of the most successful applications in mobile networks. Mobile edge servers are significantly contributing to the improvement of this type of applications, by also performing resolution adaptations as a function of the radio link quality observed by the users. In this paper, we face the problem of dynamically tracking the perceived video resolution by mobile clients in a mobile edge environment to guarantee an agreed Service Level Agreement (SLA). To this purpose, we propose a protocol-agnostic approach, based on monitoring some memory metrics of a running video streaming process at the mobile client, for identifying the time-varying resolution of the video content.
First and second order rational solutions to the Johnson equation and rogue waves
2018
Rational solutions to the Johnson equation are constructed as a quotient of two polynomials in x, y and t depending on several real parameters. We obtain an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, and t, 4N (N + 1) in y, depending on 2N − 2 real parameters for each positive integer N. We construct explicit expressions of the solutions in the cases N = 1 and N = 2 which are given in the following. We study the evolution of the solutions by constructing the patterns of their modulus in the (x, y) plane, and this for different values of parameters.