Existence and Regularity Results for Some Shape Optimization Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Existence and Regularity Results for Some Shape Optimization Problems write by Bozhidar Velichkov. This book was released on 2015-03-21. Existence and Regularity Results for Some Shape Optimization Problems available in PDF, EPUB and Kindle. We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schrödinger operators. The domains are subject to perimeter and volume constraints; we also take into account the possible presence of geometric obstacles. We investigate the properties of the optimal sets and of the optimal state functions. In particular, we prove that the eigenfunctions are Lipschitz continuous up to the boundary and that the optimal sets subject to the perimeter constraint have regular free boundary. We also consider spectral optimization problems in non-Euclidean settings and optimization problems for potentials and measures, as well as multiphase and optimal partition problems.
New Trends in Shape Optimization
New Trends in Shape Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook New Trends in Shape Optimization write by Aldo Pratelli. This book was released on 2015-12-01. New Trends in Shape Optimization available in PDF, EPUB and Kindle. This volume reflects “New Trends in Shape Optimization” and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.
Regularity of the One-phase Free Boundaries
Regularity of the One-phase Free Boundaries - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Regularity of the One-phase Free Boundaries write by Bozhidar Velichkov. This book was released on 2023-02-24. Regularity of the One-phase Free Boundaries available in PDF, EPUB and Kindle. This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research. The exposition is organized around four main theorems, which are dedicated to the one-phase functional in its simplest form. Many of the methods and the techniques presented here are very recent and were developed in the context of different free boundary problems. We also give the detailed proofs of several classical results, which are based on some universal ideas and are recurrent in the free boundary, PDE and the geometric regularity theories. This book is aimed at graduate students and researches and is accessible to anyone with a moderate level of knowledge of elliptical PDEs.
Non-Smooth and Complementarity-Based Distributed Parameter Systems
Non-Smooth and Complementarity-Based Distributed Parameter Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non-Smooth and Complementarity-Based Distributed Parameter Systems write by Michael Hintermüller. This book was released on 2022-02-18. Non-Smooth and Complementarity-Based Distributed Parameter Systems available in PDF, EPUB and Kindle. Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.
Recent Advances in Partial Differential Equations and Applications
Recent Advances in Partial Differential Equations and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recent Advances in Partial Differential Equations and Applications write by Vicenţiu D. Rădulescu. This book was released on 2016-06-28. Recent Advances in Partial Differential Equations and Applications available in PDF, EPUB and Kindle. This volume contains the proceedings of the International Conference on Recent Advances in PDEs and Applications, in honor of Hugo Beirão da Veiga's 70th birthday, held from February 17–21, 2014, in Levico Terme, Italy. The conference brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide-ranging influence of Hugo Beirão da Veiga on the field of partial differential equations, in particular those related to fluid dynamics. In his own work, da Veiga has been a seminal influence in many important areas: Navier-Stokes equations, Stokes systems, non-Newtonian fluids, Euler equations, regularity of solutions, perturbation theory, vorticity phenomena, and nonlinear potential theory, as well as various degenerate or singular models in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume.
