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This book offers a systematic treatment of a classic topic in Analysis. It fills a gap in the existing literature by presenting in detail the classic -Hölder condition and introducing the notion of locally Hölder-continuous function in an open set in Rn. Further, it provides the essential notions of multidimensional geometry applied to analysis.
Written in an accessible style and with proofs given as clearly as possible, it is a valuable resource for graduate students in Mathematical Analysis and researchers dealing with Hölder-continuous functions and their applications.
List of contents
Hölder and locally Hölder continuous functions.- Coordinate changes in Rn. Rotations. Cones in Rn.- Open sets with boundary of class Ck and of classCk. The cone property.- Open sets of class Ck and of class Ck.- Majorization formulas for functions.
About the author
Renato Fiorenza has been a professor in mathematical analysis at the University of Naples (Italy) "Federico II" since 1967. He became a professor when Italy was leading the field with Miranda, Caccioppoli, De Giorgi (who solved Hilbert's 19th problem, proving that for a class of elliptic partial differential equations with analytic coefficients the solutions had first derivatives which are Hölder continuous). Renato Fiorenza was an assistant of Caccioppoli. In his career he has established some important results about oblique derivative problems for partial differential equations.
Summary
This book offers a systematic treatment of a classic topic in Analysis. It fills a gap in the existing literature by presenting in detail the classic λ-Hölder condition and introducing the notion of locally Hölder-continuous function in an open set Ω in Rn. Further, it provides the essential notions of multidimensional geometry applied to analysis.
Written in an accessible style and with proofs given as clearly as possible, it is a valuable resource for graduate students in Mathematical Analysis and researchers dealing with Hölder-continuous functions and their applications.
