@article{FedchenkoTarkhanov2017, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {A Rado theorem for the porous medium equation}, series = {Boletin de la Sociedad Matem{\´a}tica Mexicana}, volume = {24}, journal = {Boletin de la Sociedad Matem{\´a}tica Mexicana}, number = {2}, publisher = {Springer}, address = {Cham}, issn = {1405-213X}, doi = {10.1007/s40590-017-0169-3}, pages = {427 -- 437}, year = {2017}, abstract = {We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi.}, language = {en} } @article{LyTarkhanov2016, author = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich}, title = {A Rado theorem for p-harmonic functions}, series = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana}, volume = {22}, journal = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana}, publisher = {Springer}, address = {Basel}, issn = {1405-213X}, doi = {10.1007/s40590-016-0109-7}, pages = {461 -- 472}, year = {2016}, abstract = {Let A be a nonlinear differential operator on an open set X subset of R-n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A(u) = 0 in XS of class F satisfies this equation weakly in all of X. For the most extensively studied classes F, we show conditions on S which guarantee that S is removable for F relative to A.}, language = {en} } @unpublished{LyTarkhanov2015, author = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich}, title = {A Rad{\´o} theorem for p-harmonic functions}, volume = {4}, number = {3}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-71492}, pages = {10}, year = {2015}, abstract = {Let A be a nonlinear differential operator on an open set X in R^n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A (u) = 0 in the complement of S of class F satisfies this equation weakly in all of X. For the most extensively studied classes F we show conditions on S which guarantee that S is removable for F relative to A.}, language = {en} }