Formulas for the curvature and the length of isocline lines in terms of the curvatures k, j of the level curves and of the steepest descent lines of u are given. The special case when all isoclines are straight lines is studied. Sharp bounds for functionalsl of the lengths of the isoclines lines of quasi convex and convex functions are also obtained.
On isocline lines for functions and convex stratifications of two variables / M.Longinetti; P.Manselli; A.Venturi. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - ELETTRONICO. - 89:(2010), pp. 717-743. [10.1080/00036811003627591]
On isocline lines for functions and convex stratifications of two variables
LONGINETTI, MARCO;MANSELLI, PAOLO;VENTURI, ADRIANA
2010
Abstract
Formulas for the curvature and the length of isocline lines in terms of the curvatures k, j of the level curves and of the steepest descent lines of u are given. The special case when all isoclines are straight lines is studied. Sharp bounds for functionalsl of the lengths of the isoclines lines of quasi convex and convex functions are also obtained.
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