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Regularity of minimizers of some integral functionals with degenerate integrands
Nonlinear Analysis: Theory, Methods & Applications, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
CATALDO V +2 more
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Reduction of Algebraic Integrands to Jacobian Elliptic Functions
1954The most general elliptic integral encountered in practice may appear in the form 200.00 (200.00) where R1, R2, R3 and R4 are rational integral functions of t, and where P is a polynomial of the third or fourth degree with real coefficients and no repeated factors.
Paul F. Byrd, Morris D. Friedman
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Reduction of Trigonometric Integrands to Jacobian Elliptic Functions
1954Various elliptic integrals involving trigonometric integrands occur in many geometrical and physical problems. In order to evaluate a variety of these we again find it convenient to express them in terms of integrals involving Jacobian elliptic functions.
Paul F. Byrd, Morris D. Friedman
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On bi-orthogonal systems of trigonometric functions and quadrature formulas for periodic integrands
Numerical Algorithms, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ruymán Cruz-Barroso +2 more
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SIAM Journal on Control and Optimization, 1981
A new approach to the lower semicontinuity of integral functionals is presented. By a topological embedding of the “control” and “state” spaces in the Hilbert cube and a simultaneous relaxation of the “control functions,” a powerful approach emerges whose main features include: (i) A generalized convexity condition is imposed upon the integrand of ...
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A new approach to the lower semicontinuity of integral functionals is presented. By a topological embedding of the “control” and “state” spaces in the Hilbert cube and a simultaneous relaxation of the “control functions,” a powerful approach emerges whose main features include: (i) A generalized convexity condition is imposed upon the integrand of ...
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Mathematics of Operations Research, 1991
Given a sequence of unbounded convex random sets, we study under which conditions Fatou's lemma for the weak upper limit of their conditional expectations holds. We also give multivalued versions of dominated and monotone convergence theorems, and we discuss the special case of the integral.
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Given a sequence of unbounded convex random sets, we study under which conditions Fatou's lemma for the weak upper limit of their conditional expectations holds. We also give multivalued versions of dominated and monotone convergence theorems, and we discuss the special case of the integral.
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Evaluating the Superposition Integrals by Retaining the Singularity Functions in the Integrands
IEEE Transactions on Education, 1963This paper shows how the superposition integrals can be evaluated without recourse to changing the limits of integration, when the integrands are zero over a range, through the use of singularity functions. This method avoids the need for sketching the integrands and illustrates the concepts involved in the superposition integrals without restricting ...
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Integral functionals, normal integrands and measurable selections
1976Abstract : A fundamental notion in many areas of mathematics, including optimal control, stochastic programming, and the study of partial differential equations, is that of an integral functional. By this is meant an expression of the form If(x) = integral over S of f(s,x(s))mu(DS), x is a member of X where X is a linear space of measurable functions ...
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On functionals with convex Carathéodory integrands with a linear growth condition
Journal of Mathematical Analysis and Applications, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A counter-example in homogenization of functional with polynomial integrand
1995The author considers the classical problem of homogenization in the calculus of variations \[ f_{\hom}(\xi)= \inf\Biggl\{\int_Y f(x,Du(x)) dx\mid u\in W^{1,p}_{\text{loc}}(\mathbb{R}^n), Du\text{ is }Y\text{-periodic}, \langle Du\rangle= \xi\Biggr\}, \] where \(Y\) denotes the unit cube in \(\mathbb{R}^n\) and \(\langle\cdots\rangle\) denotes the ...
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