Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side.
 A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary.
 Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields.

Blow-up Theory for Elliptic PDEs in Riemannian Geometry (Mathematical Notes, 45)

Science & Math

Hebey, Emmanuel

Robert, Frédéric

Druet, Olivier

Mathematics

Princeton University Press

In this magnificent volume, the second in the Grand Livre de Cuisine series, celebrated chefs Alain Ducasse and Frédéric Robert comprehensively cover the art of making desserts, pastries, candy, and other sweets. Everything is here— mousses and fondants; cookies and cakes; ice creams and sorbets; bonbons and nougats; fruit tarts, profiteroles, and sweet crèpes. The book’s 250 mouth-watering recipes range from traditional treats such as peach melba, candied apples, and oeufs à la neige to audacious concoctions such as tropical fruit– stuffed ravioli and coconut-encrusted lollipops. Decidedly French yet international in flavor, the book presents the authors’ masterful takes on American cheesecake; Italian cannolis, zuppa inglese, and tiramisù; and the Austrian confections known as viennoiseries. Organized by main ingredient, the Grand Livre’s structure epitomizes Ducasse’s philosophy of cooking and baking, which holds that culinary techniques should accentuate and enhance an ingredient’s true nature—not mask it. The book features more than 650 color photographs, including a full-page, close-up photo of each finished dish. Cross-sectional drawings clearly display the internal “architecture” of some of the more complex creations.

Grand Livre de Cuisine: Alain Ducasse's Desserts and Pastries

Cookbooks, Food & Wine

Ducasse, Alain

Baking

Stewart, Tabori and Chang

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