Enrico Valdinoci's Books

Partial Differential Equations and Geometric Measure Theory

Cetraro, Italy 2014

By: Alessio Figalli,Enrico Valdinoci,Ireneo Peral

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Partial Differential Equations and Geometric Measure Theory

Cetraro, Italy 2014

By: Alessio Figalli,Enrico Valdinoci,Ireneo Peral

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.

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Page Count

224

Publisher

Springer

Published Date

ISBN 10

3319740423

ISBN 13

9783319740423

Elliptic Partial Differential Equations From An Elementary Viewpoint: A Fresh Glance At The Classical Theory

By: Serena Dipierro,Enrico Valdinoci

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Elliptic Partial Differential Equations From An Elementary Viewpoint: A Fresh Glance At The Classical Theory

By: Serena Dipierro,Enrico Valdinoci

This is a textbook that covers several selected topics in the theory of elliptic partial differential equations which can be used in an advanced undergraduate or graduate course.The book considers many important issues such as existence, regularity, qualitative properties, and all the classical topics useful in the wide world of partial differential equations. It also includes applications with interesting examples.The structure of the book is flexible enough to allow different chapters to be taught independently.The book is friendly, welcoming, and written for a newcomer to the subject.It is essentially self-contained, making it easy to read, and all the concepts are fully explained from scratch, combining intuition and rigor, and therefore it can also be read independently by students, with limited or no supervision.

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Page Count

670

Publisher

World Scientific

Published Date

ISBN 10

9811290814

ISBN 13

9789811290817

Nonlocal Diffusion and Applications

By: Claudia Bucur,Enrico Valdinoci

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Nonlocal Diffusion and Applications

By: Claudia Bucur,Enrico Valdinoci

Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.

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Page Count

165

Publisher

Springer

Published Date

ISBN 10

3319287397

ISBN 13

9783319287393

Local Density of Solutions to Fractional Equations

By: Alessandro Carbotti,Serena Dipierro,Enrico Valdinoci

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Local Density of Solutions to Fractional Equations

By: Alessandro Carbotti,Serena Dipierro,Enrico Valdinoci

This book presents in a detailed and self-contained way a new and important density result in the analysis of fractional partial differential equations, while also covering several fundamental facts about space- and time-fractional equations.

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Page Count

185

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110661314

ISBN 13

9783110661316

Fractional Elliptic Problems with Critical Growth in the Whole of $\R^n$

By: Serena Dipierro,María Medina,Enrico Valdinoci

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Fractional Elliptic Problems with Critical Growth in the Whole of $\R^n$

By: Serena Dipierro,María Medina,Enrico Valdinoci

These lecture notes are devoted to the analysis of a nonlocal equation in the whole of Euclidean space. In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary. The results presented are original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.

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Page Count

162

Publisher

Springer

Published Date

ISBN 10

8876426019

ISBN 13

9788876426018

Flat Level Set Regularity of $p$-Laplace Phase Transitions

By: Enrico Valdinoci,Berardino Sciunzi,Vasile Ovidiu Savin

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Flat Level Set Regularity of $p$-Laplace Phase Transitions

By: Enrico Valdinoci,Berardino Sciunzi,Vasile Ovidiu Savin

We prove a Harnack inequality for level sets of $p$-Laplace phase transition minimizers. In particular, if a level set is included in a flat cylinder, then, in the interior, it is included in a flatter one. The extension of a result conjectured by De Giorgi and recently proven by the third author for $p=2$ follows.

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