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Using the Il'in integral representation of functions, imbedding theorems for weighted anisotropic Sobolev spaces in 𝔼ⁿ are proved. By the weight we assume a power function of the distance from an (n-2)-dimensional subspace passing through the domain considered.
Wojciech M. Zajączkowski. "On imbedding theorems for weighted anisotropic Sobolev spaces." Applicationes Mathematicae 29.1 (2002): 51-63. <http://eudml.org/doc/279741>.
@article{WojciechM2002, abstract = {Using the Il'in integral representation of functions, imbedding theorems for weighted anisotropic Sobolev spaces in 𝔼ⁿ are proved. By the weight we assume a power function of the distance from an (n-2)-dimensional subspace passing through the domain considered.}, author = {Wojciech M. Zajączkowski}, journal = {Applicationes Mathematicae}, keywords = {weighted Sobolev spaces; imbedding theorems; anisotropic Sobolev spaces}, language = {eng}, number = {1}, pages = {51-63}, title = {On imbedding theorems for weighted anisotropic Sobolev spaces}, url = {http://eudml.org/doc/279741}, volume = {29}, year = {2002}, }
TY - JOUR AU - Wojciech M. Zajączkowski TI - On imbedding theorems for weighted anisotropic Sobolev spaces JO - Applicationes Mathematicae PY - 2002 VL - 29 IS - 1 SP - 51 EP - 63 AB - Using the Il'in integral representation of functions, imbedding theorems for weighted anisotropic Sobolev spaces in 𝔼ⁿ are proved. By the weight we assume a power function of the distance from an (n-2)-dimensional subspace passing through the domain considered. LA - eng KW - weighted Sobolev spaces; imbedding theorems; anisotropic Sobolev spaces UR - http://eudml.org/doc/279741 ER -