scholarly journals Neumann problem for Monge-Ampere type equations revisited.

10.53733/176 ◽  
2021 ◽  
Vol 52 ◽  
pp. 671-689
Author(s):  
Neil Trudinger ◽  
Feida Jiang
Keyword(s):  
Neumann Problem ◽  
A Priori ◽  
Second Order ◽  
Order Derivative ◽  
Dimensional Euclidean Space ◽  
Complete Proof ◽  
Estimates Of Solutions ◽  
Derivative Estimate ◽  
Elliptic Solutions ◽  
Linearized Operator

This paper concerns  a priori second order derivative estimates of solutions of the Neumann problem for the Monge-Amp\`ere type equations in bounded domains in n dimensional Euclidean space. We first establish a double normal second order derivative estimate on the boundary under an appropriate notion of domain convexity. Then, assuming a barrier condition for the linearized operator, we provide a complete proof of the global second derivative estimate for elliptic solutions, as previously studied in our earlier work. We also consider extensions to the degenerate elliptic case, in both the regular and strictly regular matrix cases.

A priori estimates of solutions of nonlinear boundary value problems for singular in a phase variable second order differential inequalities

2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Ivan Kiguradze
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Second Order ◽  
Phase Variable ◽  
Differential Inequalities ◽  
Nonlinear Boundary Value Problems ◽  
Estimates Of Solutions ◽  
Priori Estimates

Abstract.For singular in a phase variable second order differential inequalities, a priori estimates of positive solutions, satisfying nonlinear nonlocal boundary conditions, are established.

Even (Mixed) Risk Lovers are Prudent

2013 ◽  
Vol 103 (4) ◽  
pp. 1529-1535 ◽  
Author(s):  
David Crainich ◽  
Louis Eeckhoudt ◽  
Alain Trannoy
Keyword(s):  
Utility Function ◽  
A Priori ◽  
Second Order ◽  
Order Derivative ◽  
Precautionary Savings ◽  
Positive Sign

The purpose of this note is to analyze properties of the risk lovers' utility function beyond the positive sign of its second order derivative. We show that—contrarily to a priori beliefs—risk lovers are prudent and are willing to accumulate precautionary savings. (JEL D81)

scholarly journals Positive solutions of a second-order nonlinear Robin problem involving the first-order derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhilin Yang
Keyword(s):  
Positive Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Index Theory ◽  
Second Order ◽  
Iterative Sequence ◽  
Order Derivative ◽  
Robin Problem ◽  
First Order ◽  
Fixed Point Index Theory

AbstractThis paper is concerned with the second-order nonlinear Robin problem involving the first-order derivative: $$ \textstyle\begin{cases} u''+f(t,u,u^{\prime })=0, \\ u(0)=u'(1)-\alpha u(1)=0,\end{cases} $$ { u ″ + f ( t , u , u ′ ) = 0 , u ( 0 ) = u ′ ( 1 ) − α u ( 1 ) = 0 , where $f\in C([0,1]\times \mathbb{R}^{2}_{+},\mathbb{R}_{+})$ f ∈ C ( [ 0 , 1 ] × R + 2 , R + ) and $\alpha \in ]0,1[$ α ∈ ] 0 , 1 [ . Based on a priori estimates, we use fixed point index theory to establish some results on existence, multiplicity and uniqueness of positive solutions thereof, with the unique positive solution being the limit of of an iterative sequence. The results presented here generalize and extend the corresponding ones for nonlinearities independent of the first-order derivative.

Philosophical Reduction(ism) in Meta-Language Reconstructions of Yhwh as Religious Object

2018 ◽  
Vol 26 (2) ◽  
Author(s):  
Jaco W Gericke
Keyword(s):  
Old Testament ◽  
Hebrew Bible ◽  
A Priori ◽  
Research Problem ◽  
Second Order ◽  
Unified Theory ◽  
Ontological Status ◽  
Introductory Overview ◽  
Theory Of Everything ◽  
Interpretative Approach

In Hebrew Bible/Old Testament scholarship, one encounters a variety of reductive perspectives on what exactly Yahweh as religious object is assumed to be. In this article, a clarification of the research problem is followed by an introductory overview of what is currently available on this topic as is attested in the context of various interpretative methodologies and their associated meta-languages. It is argued that any attempt to describe the actual metaphysical nature and ontological status of the religious object in the jargon of a particular interpretative approach is forever prone to committing the fallacy of reductionism. Even so, given the irreducible methodological perspectivism supervening on heuristic specificity, reductive accounts as such are unavoidable. If this is correct, then it follows a fortiori that a unified theory (of everything Yahweh can be said to be) and an ideal meta-language (with which to perfectly reconstruct the religious object within second-order discourse) are a priori impossible.

scholarly journals Plasma parameter profile inference from limited data utilizing second-order derivative priors and physic-based constraints

2021 ◽  
Vol 28 (3) ◽  
pp. 032504
Author(s):  
T. Nishizawa ◽  
M. Cavedon ◽  
R. Dux ◽  
F. Reimold ◽  
U. von Toussaint ◽  
...  
Keyword(s):  
Plasma Parameter ◽  
Second Order ◽  
Order Derivative ◽  
Limited Data ◽  
Parameter Profile

scholarly journals Estimation of Tadalafil Using Derivative Spectrophotometry in Bulk Material and in Pharmaceutical Formulation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Zamir G. Khan ◽  
Amod S. Patil ◽  
Atul A. Shirkhedkar
Keyword(s):  
Wavelength Range ◽  
Area Under Curve ◽  
Pharmaceutical Formulation ◽  
Second Order ◽  
Order Derivative ◽  
Uv Spectrophotometry ◽  
First Order ◽  
Beer's Law ◽  
Beer’S Law ◽  
Derivative Uv Spectrophotometry

Four simple, rapid, accurate, precise, reliable, and economical UV-spectrophotometric methods have been proposed for the determination of tadalafil in bulk and in pharmaceutical formulation. “Method A” is first order derivative UV spectrophotometry using amplitude, “method B” is first order derivative UV spectrophotometry using area under curve technique, “method C” is second order derivative UV spectrophotometry using amplitude, and “method D” is second order derivative UV spectrophotometry using area under curve technique. The developed methods have shown best results in terms of linearity, accuracy, precision, and LOD and LOQ for bulk drug and marketed formulation as well. In N,N-dimethylformamide, tadalafil showed maximum absorbance at 284 nm. For “method A” amplitude was recorded at 297 nm while for “method B” area under curve was integrated in the wavelength range of 290.60–304.40 nm. For “method C” amplitude was measured at 284 nm while for “method D” area under curve was selected in the wavelength range of 280.80–286.20 nm. For methods A and B, tadalafil obeyed Lambert-Beer’s law in the range of 05–50 μg/mL while for “methods C and D”, tadalafil obeyed Lambert-Beer’s law in the range of 20–70 μg/mL, and-for “methods A, B, C, and D” the correlation coefficients were found to be > than 0.999.

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