000			02070 a2200241 4500
003			OSt
005			20250210172101.0
008			250205b xxu||||| |||| 00| 0 eng d
020			_a9781470472535
040			_cIIT Kanpur
041			_aeng
082			_a515.782 _bL554f
100			_aLeoni, Giovanni
245			_aA first course in fractional Sobolev spaces _cGiovanni Leoni
260			_bAmerican Mathematical Society _c2023 _aProvidence
300			_axv, 586p
440			_aGraduate studies in mathematics
490			_v; no.229
520			_aThis book provides a gentle introduction to fractional Sobolev spaces which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It covers the definition, standard properties, extensions, embeddings, Hardy inequalities, and interpolation inequalities. The second part deals with fractional Sobolev spaces of several variables. The author studies completeness, density, homogeneous fractional Sobolev spaces, embeddings, necessary and sufficient conditions for extensions, Gagliardo-Nirenberg type interpolation inequalities, and trace theory. The third part explores some applications: interior regularity for the Poisson problem with the right-hand side in a fractional Sobolev space and some basic properties of the fractional Laplacian. The first part of the book is accessible to advanced undergraduates with a strong background in integration theory; the second part, to graduate students having familiarity with measure and integration and some functional analysis. Basic knowledge of Sobolev spaces would help, but is not necessary. The book can also serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines with a solid mathematics background. It contains several exercises and is self-contained.
650			_aFunction spaces
650			_aSobolev spaces
942			_cBK
999			_c567159 _d567159