Relevant bibliographies by topics / Lavrentiev phenomenon

Academic literature on the topic 'Lavrentiev phenomenon'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Lavrentiev phenomenon"

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Loewen, Philip D. "On The Lavrentiev Phenomenon." Canadian Mathematical Bulletin 30, no. 1 (March 1, 1987): 102–8. http://dx.doi.org/10.4153/cmb-1987-015-7.

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Cesari, L., and T. S. Angell. "On the Lavrentiev phenomenon." Calcolo 22, no. 1 (January 1985): 17–29. http://dx.doi.org/10.1007/bf02576198.

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Zolezzi, Tullio. "Wellposedness and the Lavrentiev Phenomenon." SIAM Journal on Control and Optimization 30, no. 4 (July 1992): 787–99. http://dx.doi.org/10.1137/0330043.

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Carstensen, C., and C. Ortner. "Analysis of a Class of Penalty Methods for Computing Singular Minimizers." Computational Methods in Applied Mathematics 10, no. 2 (2010): 137–63. http://dx.doi.org/10.2478/cmam-2010-0008.

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AbstractAmongst the more exciting phenomena in the field of nonlinear partial differential equations is the Lavrentiev phenomenon which occurs in the calculus of variations. We prove that a conforming finite element method fails if and only if the Lavrentiev phenomenon is present. Consequently, nonstandard finite element methods have to be designed for the detection of the Lavrentiev phenomenon in the computational calculus of variations. We formulate and analyze a general strategy for solving variational problems in the presence of the Lavrentiev phenomenon based on a splitting and penalization strategy. We establish convergence results under mild conditions on the stored energy function. Moreover, we present practical strategies for the solution of the discretized problems and for the choice of the penalty parameter.
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BAI, YU, and ZHI-PING LI. "A TRUNCATION METHOD FOR DETECTING SINGULAR MINIMIZERS INVOLVING THE LAVRENTIEV PHENOMENON." Mathematical Models and Methods in Applied Sciences 16, no. 06 (June 2006): 847–67. http://dx.doi.org/10.1142/s0218202506001376.

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A numerical method using the truncation technique on the integrand is developed for computing singular minimizers or singular minimizing sequences in variational problems involving the Lavrentiev phenomenon. It is proved that the method can detect absolute minimizers with various singularities whether the Lavrentiev phenomenon is involved or not. It is also proved that, when the absolute infimum is not attainable, the method can produce minimizing sequences. Numerical results on Manià's example and a two-dimensional problem involving the Lavrentiev phenomenon with continuous Sobolev exponent dependence, are given to show the efficiency of the method.
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BAI, YU, and ZHIPING LI. "NUMERICAL SOLUTION OF NONLINEAR ELASTICITY PROBLEMS WITH LAVRENTIEV PHENOMENON." Mathematical Models and Methods in Applied Sciences 17, no. 10 (October 2007): 1619–40. http://dx.doi.org/10.1142/s0218202507002406.

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A convergence theory is established for a truncation method in solving polyconvex elasticity problems involving the Lavrentiev phenomenon. Numerical results on a recent example by Foss et al., which has a polyconvex integrand and admits continuous singular minimizers, not only verify our convergence theorems but also provide a sharper estimate on the upper bound of a perturbation parameter for the existence of the Lavrentiev phenomenon in the example.
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Foss, M., W. Hrusa, and V. J. Mizel. "The Lavrentiev Phenomenon in Nonlinear Elasticity." Journal of Elasticity 72, no. 1-3 (2003): 173–81. http://dx.doi.org/10.1023/b:elas.0000018778.53392.b7.

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Carlson, Dean A. "Property (D) and the Lavrentiev phenomenon." Applicable Analysis 95, no. 6 (September 28, 2015): 1214–27. http://dx.doi.org/10.1080/00036811.2015.1057703.

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Gratwick, Richard. "Singular sets and the Lavrentiev phenomenon." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 3 (June 2015): 513–33. http://dx.doi.org/10.1017/s0308210513001510.

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We show that non-occurrence of the Lavrentiev phenomenon does not imply that the singular set is small. Precisely, given a compact Lebesgue null subsetE⊆ ℝ and an arbitrary superlinearity, there exists a smooth strictly convex Lagrangian with this superlinear growth such that all minimizers of the associated variational problem have singular set exactlyEbut still admit approximation in energy by smooth functions.
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Heinricher, Arthur C., and Victor J. Mizel. "A New Example of the Lavrentiev Phenomenon." SIAM Journal on Control and Optimization 26, no. 6 (November 1988): 1490–503. http://dx.doi.org/10.1137/0326087.

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Dissertations / Theses on the topic "Lavrentiev phenomenon"

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BONFANTI, GIOVANNI. "Progresses on some classical problems of the calculus of variations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2012. http://hdl.handle.net/10281/28223.

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Some theorems about the validity of the Euler-Lagrange equation are proved. In particular, Lagrangians without regularity hypothesis or without growth assumptions are considered. Moreover, a result about the non-occurrence of the Lavrentiev phenomenon in the scalar case is proved.
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Book chapters on the topic "Lavrentiev phenomenon"

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Zaslavski, Alexander J. "Generic Nonoccurrence of the Lavrentiev Phenomenon." In Nonconvex Optimal Control and Variational Problems, 233–53. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7378-7_8.

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Heinricher, A. C., and V. J. Mizel. "The Lavrentiev Phenomenon for Invariant Variational Problems." In Analysis and Continuum Mechanics, 709–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83743-2_38.

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Zaslavski, Alexander J. "Nonoccurrence of the Lavrentiev Phenomenon for Variational Problems." In Nonconvex Optimal Control and Variational Problems, 159–95. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7378-7_6.

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Zaslavski, Alexander J. "Nonoccurrence of the Lavrentiev Phenomenon in Optimal Control." In Nonconvex Optimal Control and Variational Problems, 197–231. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7378-7_7.

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Mizel, Victor. "Recent Progress on the Lavrentiev Phenomenon with Applications." In Differential Equations And Control Theory. CRC Press, 2001. http://dx.doi.org/10.1201/9780203902189.ch18.

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Ruiz Goldstein, Gisèle, Jerome A. Goldstein, and Chien-an Lung. "Nuclear Cusps, Magnetic Fields and the Lavrentiev Phenomenon In Thomas-Fermi Theory." In Mathematics in Science and Engineering, 141–51. Elsevier, 1993. http://dx.doi.org/10.1016/s0076-5392(08)62377-2.

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Conference papers on the topic "Lavrentiev phenomenon"

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Eide, Joseph, and Anil V. Rao. "Lavrentiev Phenomenon inhpGaussian Quadrature Collocation Methods for Optimal Control." In AIAA/AAS Astrodynamics Specialist Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2016. http://dx.doi.org/10.2514/6.2016-5575.

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Bai, Yu. "Numerical Methods for Detecting Singular Set Involving the Lavrentiev Phenomenon." In 2009 International Conference on Information Engineering and Computer Science. IEEE, 2009. http://dx.doi.org/10.1109/iciecs.2009.5365518.

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Eide, Joseph D., William W. Hager, and Anil V. Rao. "Modified Radau Collocation method for Solving Optimal Control Problems with Nonsmooth Solutions Part I: Lavrentiev Phenomenon and the Search Space." In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8619830.

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