000			02091 a2200265 4500
003			OSt
005			20250210172152.0
008			250206b xxu||||| |||| 00| 0 eng d
020			_a9781470477028
040			_cIIT Kanpur
041			_aeng
082			_a515.782 _bL554f2
100			_aLeoni, Giovanni
245			_a A first course in Sobolev spaces [2nd ed.] _cGiovanni Leoni
250			_a2nd ed.
260			_bAmerican Mathematical Society _aProvidence _c2017
300			_axxii, 734p
440			_aGraduate studies in mathematics
490			_v; no.181
520			_aThis book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue-Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions. The remaining chapters are a treatise on Sobolev functions. The second edition focuses more on higher order derivatives and it includes the interpolation theorems of Gagliardo and Nirenberg. It studies embedding theorems, extension domains, chain rule, superposition, Poincare's inequalities and traces. A major change compared to the first edition is the chapter on Besov spaces, which are now treated using interpolation theory.
650			_aFunctional analysis
650			_aSobolev spaces
650			_aPartial differential equations
942			_cBK
999			_c567160 _d567160