An elementary proof of the Brezis and Mironescu theorem on the composition operator in fractional Sobolev spaces

Journal of Evolution Equations

Volumn 2, Issue 1, 2002, Pages 113-125

  Maz'ya, V ^a   Shaposhnikova, T ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Composition operator; Fractional Sobolev spaces; Gagliardo Nirenberg inequalities; Pointwise interpolation inequalities

Indexed keywords

EID: 0345754509     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-002-8082-1     Document Type: Article

References (6)

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2. BREZIS, H. and MIRONESCU, P., Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces, J. Evolution Equations 1 (2001) no. 4,387-404.
3. HEDBERG, L.-I., On certain convolution inequalities, Proc. Amer. Math. Soc. 36 (1972) no. 2, 505-510.
4. MAZ'YA, V. and SHAPOSHNIKOVA, T., On pointwise interpolation inequalities for derivatives, Mathematica Bohemica 124 (1999) no. 2-3,131-148.
5. MAZ'YA, V. and POBORCHI, S., Differentiable functions on bad domains, World Scientific Publishing, Singapore, 1997.
6. RUNST, T. and SICKEL, W., Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations, Walter de Gruyter, Berlin-New York, 1996.