{ "item_title" : "Nonlocal Diffusion and Applications", "item_author" : [" Claudia Bucur", "Enrico Valdinoci "], "item_description" : "Introduction.- 1 A probabilistic motivation.-1.1 The random walk with arbitrarily long jumps.- 1.2 A payoff model.-2 An introduction to the fractional Laplacian.-2.1 Preliminary notions.- 2.2 Fractional Sobolev Inequality and Generalized Coarea Formula.- 2.3 Maximum Principle and Harnack Inequality.- 2.4 An s-harmonic function.- 2.5 All functions are locally s-harmonic up to a small error.- 2.6 A function with constant fractional Laplacian on the ball.- 3 Extension problems.- 3.1 Water wave model.- 3.2 Crystal dislocation.- 3.3 An approach to the extension problem via the Fourier transform.- 4 Nonlocal phase transitions.- 4.1 The fractional Allen-Cahn equation.- 4.2 A nonlocal version of a conjecture by De Giorgi.- 5 Nonlocal minimal surfaces.- 5.1 Graphs and s-minimal surfaces.- 5.2 Non-existence of singular cones in dimension 2 5.3 Boundary regularity.- 6 A nonlocal nonlinear stationary Schr dinger type equation.- 6.1 From the nonlocal Uncertainty Principle to a fractional weighted inequality.- Alternative proofs of some results.- A.1 Another proof of Theorem A.2 Another proof of Lemma 2.3.- References.", "item_img_path" : "https://covers3.booksamillion.com/covers/bam/3/31/928/738/3319287389_b.jpg", "price_data" : { "retail_price" : "69.99", "online_price" : "69.99", "our_price" : "69.99", "club_price" : "69.99", "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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