naa a22 4500 510781535 CHVBK 20180411083249.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s11854-013-0001-6 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0001-6 Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem [Elektronische Daten] [Cristian Rios, Eric Sawyer, Richard Wheeden] In [10], we considered a class of infinitely degenerate quasilinear equations of the form div $$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0$$ and derived a priori bounds for high order derivatives D a w of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior $${\varrho ^\infty }$$ -regularity of solutions for the corresponding Dirichlet problem with continuous boundary data. Hebrew University Magnes Press, 2013 Rios Cristian University of Calgary, Calgary, Alberta, Canada aut Sawyer Eric Mcmaster University, Hamilton, Ontario, Canada aut Wheeden Richard Rutgers University, New Brunswick, N.J., USA aut Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 1-62 0021-7670 119:1<1 2013 119 11854 https://doi.org/10.1007/s11854-013-0001-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0001-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rios Cristian University of Calgary, Calgary, Alberta, Canada aut NATIONALLICENCE 700 1- Sawyer Eric Mcmaster University, Hamilton, Ontario, Canada aut NATIONALLICENCE 700 1- Wheeden Richard Rutgers University, New Brunswick, N.J., USA aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 1-62 0021-7670 119:1<1 2013 119 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer