This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.
This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory. Contents: Semi-Classical Theory; Measurable Functions; Sobolev Spaces; Convexity and Semicontinuity; Quasi-Convex Functionals; Quasi-Minima; HAlder Continuity; First Derivatives; Partial Regularity; Higher Derivatives. Readership: Graduate students, academics and researchers in the field of analysis and differential equations.
I. In this second volume, we continue at first the study of non homogeneous boundary value problems for particular classes of evolu tion equations. 1 In Chapter 4 , we study parabolic operators by the method of Agranovitch-Vishik [lJ; this is step (i) (Introduction to Volume I, Section 4), i.e. the study of regularity. The next steps: (ii) transposition, (iii) interpolation, are similar in principle to those of Chapter 2, but involve rather considerable additional technical difficulties. In Chapter 5, we study hyperbolic operators or operators well defined in thesense of Petrowski or Schroedinger. Our regularity results (step (i)) seem to be new. Steps (ii) and (iii) are all3.logous to those of the parabolic case, except for certain technical differences. In Chapter 6, the results of Chapter'> 4 and 5 are applied to the study of optimal control problems for systems governed by evolution equations, when the control appears in the boundary conditions (so that non-homogeneous boundary value problems are the basic tool of this theory). Another type of application, to the characterization of "all" well-posed problems for the operators in question, is given in the Ap pendix. Still other applications, for example to numerical analysis, will be given in Volume 3.
William Lloyd Garrison and Giuseppe Mazzini, two of the foremost radicals of the nineteenth century, lived during a time of profound economic, social, and political transformation in America and Europe. Both born in 1805, but into dissimilar family backgrounds, the American Garrison and Italian Mazzini led entirely different lives -- one as a citizen of a democratic republic, the other as an exile proscribed by most European monarchies. Using a comparative analysis, Enrico Dal Lago suggests that Garrison and Mazzini nonetheless represent a connection between the egalitarian ideologies of American abolitionism and Italian democratic nationalism. Focusing on Garrison's and Mazzini's activities and transnational links within their own milieus and in the wider international arena, Dal Lago shows why two nineteenth-century progressives and revolutionaries considered liberation from enslavement and liberation from national oppression as two sides of the same coin. At different points in their lives, both Garrison and Mazzini demonstrated this belief by concurrently supporting the abolition of slavery in the United States and the national revolutions in Italy. The two meetings Garrison and Mazzini had, in 1846 and in 1867, served to reinforce their sense that they somehow worked together toward the achievement of liberty not just in the United States and Italy, but also in the Atlantic and Euro-American world as a whole. In the end, the abolition of American slavery led to Garrison's consecration, while the new Italian kingdom forced Mazzini into exile. Despite these different outcomes, Garrison and Mazzini both attracted legions of devoted followers who believed these men personified the radical causes of the nations to which they belonged.
Non è vero che in un individuo l’equilibrio si raggiunge con l’equilibrio tra la parte maschile e la parte femminile né si sa cosa tali “parti” siano davvero. Non è vero che l’anima è un archetipo che può “far crescere” un maschio soltanto se proiettato su una donna, farlo procedere dallo stato beluino a quello di “vero uomo” o, più falso ancora, da bambino ad adulto. Semmai sono le donne a essere le eterne bambine. Non è vero che un uomo possa avere pace soltanto armonizzando in unità di tutte le componenti della psiche. Al contrario, può raggiungere se non quiete almeno dignità e rispetto per se stesso soltanto imparando a navigare tra le sue contraddizioni, nel suo caos. Un altro luogo comune da sfatare? La teoria della santificante conciliazione degli opposti. Conduce a scelte devastanti per la società e assassine per l’individuo, è la culla di ogni bastardo compromesso politico, è il frutto avvelenato del pensiero di Hegel e dell’eterno oscillare tra assolutismo assassino e lassismo scatenato proprio della sua patria tedesca. Ultima chicca: nel rapporto con i sentimenti è la donna a essere handicappata, schiava com’è delle emozioni che sono causa prima dei sentimenti stessi ma in grado, se non filtrate alchenicamente, di soffocarli sul nascere, di portare ogni individuo – donna o uomo che sia – alle scelte più sbagliate della propria vita. Erich Weisz esamina tutti questi “miti” dell’età moderna, “miti” nel senso etimologico di indiscutibili verità. Sono verità assolute come in passato lo sono state quelle che affermavano essere i negri non umani, la terra piatta, le donne inferiori quando non streghe, unico dio il dio dominante della cultura militarmente superiore. Ipotesi da cui Erich Weisz deduce essere ogni guerra una guerra tra dèi combattuta con la carne e il sangue degli umani. Tra tanti luoghi comuni incrollabili, pietrificati opinioni Erich Weisz naviga per fare aprire gli occhi del lettore sul fatto che tante devastanti menzogne sono volte a riportare al potere assoluto nella cultura occidentale una divinità arcaica ostile al maschio della specie e al progredire della specie umana. Per lui tale divinità nemica è la Grande Madre. Weisz espone il proprio eterodosso pensiero attraverso un saggio romanzato in cui compaiono dèi, oltre a uomini e donne. Gli dèi intervengono nelle loro umane vicende come facevano in remoti poemi epici o come sono sentiti vivi e presenti e vengono invocati ogni giorno in famiglie religiose d’ogni credo. Gli dèi di questa saga non sono come i pupazzi di un cartone animato o le figure costruite al computer in storie contemporanee di grande successo, in film e romanzi. Non sono mere immagini commoventi. Non offrono effetti visivi speciali in 3D, roba da videogiochi. Sono dèi veri ed eterni. Sono dèi difficili da “sentire” ma turbano quando toccano l’animo. Il loro costellarsi grazie alle righe di queste libro possono disturbare molti, come disturbano le verità più profonde, le verità che si agitano nel profondo dell’inconscio. Se inascoltate, possono persino sconvolgere, irritare, fare arrabbiare. Si sconsiglia pertanto la lettura de La Divinità Nemica a conformisti e iracondi, qualunque sia la loro età e il modo di esprimere la propria sessualità.
Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the simplest variational methods are evolving as classical tools in the field of nonlinear differential equations. This book is an introduction to variational methods and their applications to semilinear elliptic problems. Providing a comprehensive overview on the subject, this book will support both student and teacher engaged in a first course in nonlinear elliptic equations. The material is introduced gradually, and in some cases redundancy is added to stress the fundamental steps in theory-building. Topics include differential calculus for functionals, linear theory, and existence theorems by minimization techniques and min-max procedures. Requiring a basic knowledge of Analysis, Functional Analysis and the most common function spaces, such as Lebesgue and Sobolev spaces, this book will be of primary use to graduate students based in the field of nonlinear partial differential equations. It will also serve as valuable reading for final year undergraduates seeking to learn about basic working tools from variational methods and the management of certain types of nonlinear problems.
This book is a guide to Milan for a visit lasting two, three, or more days. There are extensive descriptions and photos of the attractions: museums, churches, nightlife, and other attractions. In addition, it includes descriptions of how to get to Milan, driving, parking in the city, and helpful info to stay there. The guide includes sections on day trips from Milan to visit Lake Como, Lake Maggiore, Portofino, and the art cities of Pavia, Bergamo Alta, and Vigevano. In addition, the guide contains sections covering single days or half days, so you can combine several areas depending on the length of your stay and your preference of what to see.
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.
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.
The first multimedia medical text of its kind―presenting the most comprehensive and up-to-date full-color material about robotics in General Surgery. The Foundation and Art of Robotic Surgery facilitates the learning of surgery while applying robotic technology in multiple anatomical locations, using a comprehensive, concise and practical description of each standardized surgical procedure. The book provides clear descriptions of the instrument requirements, indications and relative contraindications to the robotic approach, preoperative phases including trocar placement, patient positioning, OR set-up, and a detailed description of the operative steps. Each operation is divided into steps with specific timeframes, for learning and teaching purposes. Readers will learn how to use robots to make smaller incisions, decrease blood loss and postoperative pain, as well as foster quicker healing time and reduce hospital stays. Written by the senior editors with the contribution of internationally renowned robotic surgeons and academics, this is an invaluable resource for both beginner and experienced surgeons performing robotic procedures for the first time. The Foundation and Art of Robotic Surgery features: 900+ photos and 900+ drawings of the standard anatomy, anatomical variations and surgical maneuvers Access to 200+ videos (video clips of the main steps and full procedures videos) Fifty-one chapters covering General Principles of Robotic Surgery, Thyroid Surgery, Chest Surgery, Gastric and Bariatric Surgery, Intestinal Surgery, Spleen and Pancreas Surgery, Liver Surgery, Transplant Surgery, and more Clear, concise presentation of the instruments, tools, material, indications and relative contraindications to the robotic approach, preoperative phases and each operative steps Boxed text highlighting tips and tricks, anatomical notions, common pitfalls, editorial comments and average time frames Techniques for robotic transplant surgery, renal aneurysm repair and single port robotic surgery principles
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