Open Access
The implicit function theorem and implicit parametrizations
Dan Tiba
- 01 Jan 2013
TL;DR: A dierential equations treatment of the implicit functions problem allows a precise and complete description of the solution, of continuity and dierentiability properties, and extensions to higher dimension are possible.
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Abstract: We discuss a dierential equations treatment of the implicit functions problem. Our approach allows a precise and complete description of the solution, of continuity and dierentiability properties. The critical case is also considered. The investigation is devoted to dimension two and three, but extensions to higher dimension are possible. MSC: 26B10, 34A12, 53A05.
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Citations
Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
3.5K
Topological optimization via cost penalization
Cornel Marius Murea,Dan Tiba +1 more
TL;DR: The discretized approximating problem is introduced and an explicit construction of the associated discrete gradient is given and it is formulated as an optimal control problem.
7
Topological optimization via cost penalization
Cornel Marius Murea,Dan Tiba +1 more
TL;DR: In this article, the authors considered general shape optimization problems governed by Dirichlet boundary value problems, and formulated the problem as an optimal control problem with a discretized approximating problem.
3
•Posted Content
Implicit systems in arbitrary dimension: constructive local parametrization and generalized solutions
TL;DR: In this article, a constructive local parametrization method for solutions of general implicit systems in arbitrary dimension and the associated equation in variations is given. And the critical case of the implicit functions theorem and the notion of generalized solutions are discussed.
1
Implicit Parametrizations and Applications
Mihaela Roxana Nicolai,Dan Tiba +1 more
- 29 Jun 2015
TL;DR: This work presents the notion of generalized solution, in the critical case and indicates some numerical examples in dimension two and three, using MatLab, and introduces general optimal control formulations in the boundary observation case.
References
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Stanley Osher,James A. Sethian +1 more
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
14K
•Book
Real and complex analysis
Walter Rudin
- 01 Jan 1966
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
•Book
Optimization and nonsmooth analysis
Frank H. Clarke
- 01 Jan 1983
TL;DR: The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.
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An introduction to variational inequalities and their applications
David Kinderlehrer,Guido Stampacchia +1 more
- 01 Jan 1980
TL;DR: In this paper, the SIAM edition Preface Glossary of notations Introduction Part I. Variational Inequalities in Rn Part II. Free Boundary Problems Governed by Elliptic Equations and Systems Part VII. A One Phase Stefan Problem Bibliography Index.
4.9K
Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
3.5K