Geodesic
Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 293-303

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For irregular domains $G\subset \mathbb R^n$ satisfying the flexible $\sigma $-cone condition, we establish embedding theorems and Gagliardo–Nirenberg type multiplicative inequalities that are anisotropic with respect to the order of derivatives and integrability exponents. 
@article{TM_2015_290_a23,
     author = {A. Yu. Golovko},
     title = {Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {293--303},
     publisher = {mathdoc},
     volume = {290},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_290_a23/}
}
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A. Yu. Golovko. Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 293-303. http://geodesic.mathdoc.fr/item/TM_2015_290_a23/