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Where Does Smoothness Count the Most for Two-Point Boundary-Value Problems?
1999
Journal of Complexity
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We are concerned with the complexity of 2mth order elliptic two-point boundary-value problems Lu = f. ...
In this paper, we study problems in which f has r derivatives in the L p -sense and for L having the usual divergence form ...
Some general remarks Recall that the goal of this paper is to nd the complexity of our class of two-point boundary-value problems, as well as optimal algorithms, for the classes of continuous and standard ...
doi:10.1006/jcom.1999.0510
fatcat:jtkdqcaqrfeuzpp6ykijzhops4
The Problem of Perimeter
2018
infocus Magazine
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Few real world objects have ideal Euclidean boundaries; most reveal more and more irregularities as magnification increases. ...
When an image of the object is digitised, it becomes necessary to decide how to define the boundary and the pixels that determine it, and how to measure the boundary length. ...
Measuring the area by counting pixels gives a result for the hole of 94, which is the average of the areas within the two outlines, but the average of the two line lengths, or the length of a line midway ...
doi:10.22443/rms.inf.1.167
fatcat:zoiscygyvjdlpb7msupv6wpj64
On an overdetermined elliptic problem
2011
Pacific Journal of Mathematics
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Hence, in addition to the regular boundary F(i ,)ޒ which is a smooth periodic curve, the image of F has a singular boundary: the set of limits of F(x + i y) as u tends to +∞, for the values of y for ...
Our results raise the problem of the classification of (unbounded) smooth mdimensional exceptional manifolds. ...
doi:10.2140/pjm.2011.250.319
fatcat:jom4jvyy4nhknf6nybrwy4s3yy
Mathematical problems in transonic flow
1986
Canadian mathematical bulletin
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The problem is simplified and the important role of modifying the equations with physics terms is examined. ...
We present an outline of the problem of irrotational compressible flow past an airfoil at speeds that lie somewhere between those of the supersonic flight of the Concorde and the subsonic flight of commercial ...
Of course adding v smooths out the solution and the solution is found as the fixed point of a mapping using say the Schauder theorem. But there does not appear to be any control on the max | V(j>| . ...
doi:10.4153/cmb-1986-023-3
fatcat:7do5omn2ozhzxf2jbhyb3jm6jy
Whitham hierarchy in growth problems
2005
Theoretical and mathematical physics
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2004 accepted arXiv:math-ph/0404005v2 fatcat:hwe2a5ydarci5fltcc4yex4w4qOther Versions
This equivalence allows one to distinguish a class of exact solutions to the Laplacian growth problem in the multiply-connected case. ...
We discuss the recently established equivalence between the Laplacian growth in the limit of zero surface tension and the universal Whitham hierarchy known in soliton theory. ...
Acknowledgments The author is grateful to O.Agam, E.Bettelheim, I.Krichever, A.Marshakov, M.Mineev-Weinstein, R.Theodorescu and P.Wiegmann for collaboration and useful discussions. ...
doi:10.1007/s11232-005-0002-4
fatcat:y7gvwkoobrdb3luz7oejkhne7q
Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
2013
Inverse Problems
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2013 pre-print arXiv:1212.6785v3 fatcat:cd2l3u4ggzbodciygjddva2vgqOther Versions
Some results on the discreteness and localization of the spectrum are obtained for complex valued n(x). ...
All the results are obtained under the assumption that n(x)-1 does not vanish at the boundary of the obstacle or it vanishes identically, but its normal derivative does not vanish at the boundary. ...
Grushin [21] , [22] , who calculated the full symbols of different pseudo-differential operators that map boundary values of one problem for an elliptic equation to the boundary values of another problem ...
doi:10.1088/0266-5611/29/10/104003
fatcat:gnszfbxkw5dj3geywxyzxlpevi
Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci
[article]
2018
arXiv
pre-print
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In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. ...
The framework is then used to prove the existence of obstructions arising from conformal symplectic symmetries on the bifurcation behaviour of solutions to Hamiltonian boundary value problems. ...
Acknowledgements We thank Peter Donelan, Bernd Krauskopf, Hinke Osinga and Gemma Mason for useful discussions. This research was supported by the Marsden Fund of the Royal Society Te Apārangi. ...
arXiv:1804.07479v3
fatcat:syeyzld6l5czflcuum5aqhgyce
Vortex design problem
2012
Journal of Computational and Applied Mathematics
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In this investigation we propose a computational approach for the solution of optimal control problems for vortex systems with compactly supported vorticity. ...
Recognizing such Euler flows as free-boundary problems, the proposed approach relies on shape differentiation combined with adjoint analysis to determine cost functional gradients. ...
Acknowledgments The author wishes to thank Alan Elcrat for interesting discussions, and is also grateful to Professors Alan Elcrat and Ken Miller for providing him with the code for the solution of Euler ...
doi:10.1016/j.cam.2011.11.002
fatcat:yd4e262wv5afvdc5fn6s2vbb2y
Hyperbolic lattice point problems
2011
Proceedings of the American Mathematical Society
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We prove some analogues of planar lattice point problems replacing R 2 by the Poincaré model of the hyperbolic plane and using the orbit of a point under the modular group instead of the lattice generated ...
Acknowledgments The author is grateful to the mathematics department of Rutgers University for providing hospitality while this work was completed. The author also would like to thank E. ...
This is in fact a fundamental problem because the classic planar lattice point problem (approximate the number of lattice points in enlarging convex regions [6] ) is reduced to it after dividing the boundary ...
doi:10.1090/s0002-9939-2010-10536-1
fatcat:rdxtgprjgbavzmjxasvgqheviq
The reconstruction problem
[chapter]
2004
Series in Medical Physics and Biomedical Engineering
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For a given set of test functions v (1.45) is the weak formulation of the boundary value problem for 1.1 with current density specified on the electrodes. ...
This mixed boundary value problem is well-posed, and the resulting currents are I l = E l σ∂φ/∂n. ...
doi:10.1201/9781420034462.pt1
fatcat:zzwaarjx6jez7b7bmv267r654y
New multigrid smoothers for the Oseen problem
2010
Numerical Linear Algebra with Applications
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We investigate the performance of smoothers based on the Hermitian/skew-Hermitian (HSS) and augmented Lagrangian (AL) splittings applied to MAC discretizations of the Oseen problem. ...
Local Fourier analysis and numerical experiments on a 2-D lid-driven cavity problem indicate that the proposed smoothers result in hindependent convergence and are fairly robust with respect to the Reynolds ...
ν; see also [15] where the difficulty of smoothing for the Navier-Stokes equations with low viscosity is pointed out. ...
doi:10.1002/nla.707
fatcat:vufppcep55gqtgry3xetuhmsb4
Hilbert's 16th problem
[article]
2021
arXiv
pre-print
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The strategy of proof brings variational techniques into the differential-system field by transforming the task of counting limit cycles into counting critical points for a certain smooth, non-negative ...
We thus solve the second part of Hilbert's 16th problem providing a uniform upper bound for the number of limit cycles which only depends on the degree of the polynomial differential system. ...
A subset S ⊂ H is said to be a valley for E if it is simply connected, the boundary ∂S does not contain any of the critical points of E, and S is invariant under X(t, ·) for every small positive t, i.e ...
arXiv:2103.07193v1
fatcat:k2bm7zkac5eg3fx3t2r5ndp3ga
Scalable computation of thermomechanical turbomachinery problems
[article]
2018
arXiv
pre-print
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problems and for other physical processes, such as contact, that are important in turbomachinery analysis. ...
The performance demonstrated in this work opens up the possibility of system-level thermomechanical modelling, and lays the foundation for further research into high-performance formulations for even larger ...
Acknowledgements We thank Dr Mark Adams of Lawrence Berkeley National Laboratory for his advice on the use of smoothed aggregation AMG. ...
arXiv:1804.10060v1
fatcat:2c4sbmv7nne37iyabqunx2u62a
TURNING SHAPE DECISION PROBLEMS INTO MEASURES
2004
International journal of shape modeling
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This paper considers the problem of constructing shape measures; we start by giving a short overview of areas of practical application of such measures. ...
We give two general principles for constructing measures in this way, and show how they can be applied to construct various shape measures, including ones for convexity, circularity, ellipticity, triangularity ...
Acknowledgments We would like to thank the members of the Geometric Modelling Society for various helpful discussions, including suggesting some shape properties for measurement, and pointers to references ...
doi:10.1142/s0218654304000614
fatcat:tats7vlypbhblippicfepliwoq
A note on some overdetermined elliptic problem
[article]
2010
arXiv
pre-print
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(nonzero) Neumann condtion at the boundary. ...
We study the two-dimensional case: we present various examples and give a general construction algorithm of such surface by using complex analysis. ...
Acknowledgments : We thank Romain Dujardin and Charles Favre for useful discussions. The third author is also partially supported by the ANR-08-BLANC-0335-01 grant. ...
arXiv:1001.1060v1
fatcat:jxb54o4vvfbtvhgz6d4jofzwhu
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