{ "item_title" : "Elliptic Regularity Theory by Approximation Methods", "item_author" : [" Edgard A. Pimentel "], "item_description" : "Presenting the basics of elliptic PDEs in connection with regularity theory, the book bridges fundamental breakthroughs - such as the Krylov-Safonov and Evans-Krylov results, Caffarelli's regularity theory, and the counterexamples due to Nadirashvili and Vlăduţ - and modern developments, including improved regularity for flat solutions and the partial regularity result. After presenting this general panorama, accounting for the subtleties surrounding C-viscosity and Lp-viscosity solutions, the book examines important models through approximation methods. The analysis continues with the asymptotic approach, based on the recession operator. After that, approximation techniques produce a regularity theory for the Isaacs equation, in Sobolev and H lder spaces. Although the Isaacs operator lacks convexity, approximation methods are capable of producing H lder continuity for the Hessian of the solutions by connecting the problem with a Bellman equation. To complete the book, degenerate models are studied and their optimal regularity is described.", "item_img_path" : "https://covers2.booksamillion.com/covers/bam/1/00/909/666/1009096664_b.jpg", "price_data" : { "retail_price" : "110.00", "online_price" : "110.00", "our_price" : "110.00", "club_price" : "110.00", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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