Search results for " solution"
showing 10 items of 3084 documents
Kinetic evidence for the incorporation of the [(pentamethylcyclopentadienyl) (2,2′-bipyridyl)(aquo)rhodium(III)] complex into DPPC vesicles
2008
Abstract The binding of the [(pentamethylcyclopentadienyl) (2,2′-bipyridyl)(aquo)rhodium(III)] complex [Cp*RhIII(bpy)H2O]2+, to l -α-dipalmitoylphosphatidyl choline (DPPC) vesicles has been estimated by studying the kinetics of the electron transfer reaction between the rhodium(III) complex and formiate ions. Kinetic measurements carried out under anaerobic conditions in absence and presence of DPPC show that the total reaction is composed of two steps. The rate of the first reaction increases with the phospholipid concentration, while that of the second process is independent of the concentration of DPPC. This is consistent with a reaction, where the two reacting species are partitioned be…
Game-Theoretic Approach to Hölder Regularity for PDEs Involving Eigenvalues of the Hessian
2021
AbstractWe prove a local Hölder estimate for any exponent $0<\delta <\frac {1}{2}$ 0 < δ < 1 2 for solutions of the dynamic programming principle $$ \begin{array}{@{}rcl@{}} u^{\varepsilon} (x) = \sum\limits_{j=1}^{n} \alpha_{j} \underset{\dim(S)=j}{\inf} \underset{|v|=1}{\underset{v\in S}{\sup}} \frac{u^{\varepsilon} (x + \varepsilon v) + u^{\varepsilon} (x - \varepsilon v)}{2} \end{array} $$ u ε ( x ) = ∑ j = 1 n α j inf dim ( S ) = j sup v ∈ S | v | = 1 u ε ( x + ε v ) + u ε ( x − ε v ) 2 with α1,αn > 0 and α2,⋯ ,αn− 1 ≥ 0. The proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDE $…
Equivalence of viscosity and weak solutions for a $p$-parabolic equation
2019
AbstractWe study the relationship of viscosity and weak solutions to the equation $$\begin{aligned} \smash {\partial _{t}u-\varDelta _{p}u=f(Du)}, \end{aligned}$$ ∂ t u - Δ p u = f ( D u ) , where $$p>1$$ p > 1 and $$f\in C({\mathbb {R}}^{N})$$ f ∈ C ( R N ) satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when $$p\ge 2$$ p ≥ 2 .
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.
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…
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.