Geodesic
Functions with finite Dirichlet integral in a~domain with a~cusp at the boundary
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XII, Tome 126 (1983), pp. 117-137

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Let $\Omega$, be a bounded domain in $\mathbb R^2$, $n>2$, with inward or outward cusps at $\partial\Omega$, and let $H^1(\Omega)$ be the space of functions with finite Dirichlet integral. Our main result is a characterization of the space of traces of functions in $H^1(\Omega)$. As a corollary we obtain the existence of a continuous linear extension mapping: $H^1(\Omega)\to H^1(\mathbb R^n)$ provided the domain has an inward cusp. (It is well known that the latter fails for $n=2$). 
@article{ZNSL_1983_126_a13,
     author = {V. G. Maz'ya},
     title = {Functions with finite {Dirichlet} integral in a~domain with a~cusp at the boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {117--137},
     publisher = {mathdoc},
     volume = {126},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a13/}
}
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V. G. Maz'ya. Functions with finite Dirichlet integral in a~domain with a~cusp at the boundary. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XII, Tome 126 (1983), pp. 117-137. http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a13/