Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 885-903

IMPROVED POINCARÉ INEQUALITIES IN FRACTIONAL SOBOLEV SPACES

Irene Drelichman and Ricardo G. Durán

Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, IMAS (UBA-CONICET)
Ciudad Universitaria, 1428 Buenos Aires, Argentina; irene 'at' drelichman.com

Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, IMAS (UBA-CONICET) and Departamento de Matemática
Ciudad Universitaria, 1428 Buenos Aires, Argentina; rduran 'at' dm.uba.ar

Abstract. We obtain improved fractional Poincaré and Sobolev–Poincaré inequalities including powers of the distance to the boundary in bounded John, s-John, and Hölder-α domains, and discuss their optimality.

2010 Mathematics Subject Classification: Primary 26D10; Secondary 46E35.

Key words: Sobolev inequality, Poincaré inequality, fractional norms, weighted Sobolev spaces, John domains, s-John domains, cusp domains

Reference to this article: I. Drelichman and R. G. Durán: Improved Poincaré inequalities in fractional Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 43 (2018), 885-903.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4352