caa a22 4500 606194282 CHVBK 20210128105229.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00030-015-0315-4 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0315-4 On the viscosity solutions to Trudinger's equation [Elektronische Daten] [Tilak Bhattacharya, Leonardo Marazzi] We study the existence of positive viscosity solutions to Trudinger's equation for cylindrical domains $${\Omega\times[0, T)}$$ Ω × [ 0 , T ) , where $${\Omega\subset {I\!R}^{n}, n\ge 2,}$$ Ω ⊂ I R n , n ≥ 2 , is a bounded domain, T>0 and $${2\le p < \infty}$$ 2 ≤ p < ∞ . We show existence for general domains $${\Omega,}$$ Ω , when $${n<p<\infty}$$ n < p < ∞ . For $${2\le p\le n}$$ 2 ≤ p ≤ n , we prove existence for domains $${\Omega}$$ Ω that satisfy a uniform outer ball condition. We achieve this by constructing suitable sub-solutions and super-solutions and applying Perron's method. Springer Basel, 2015 Bhattacharya Tilak Department of Mathematics, Western Kentucky University, 42101, Bowling Green, KY, USA aut Marazzi Leonardo Department of Liberal Arts, Savannah College of Arts and Design, 31401, Savannah, GA, USA aut Nonlinear Differential Equations and Applications NoDEA Springer International Publishing 22/5(2015-10-01), 1089-1114 1021-9722 22:5<1089 2015 22 30 https://doi.org/10.1007/s00030-015-0315-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0315-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bhattacharya Tilak Department of Mathematics, Western Kentucky University, 42101, Bowling Green, KY, USA aut NATIONALLICENCE 700 1- Marazzi Leonardo Department of Liberal Arts, Savannah College of Arts and Design, 31401, Savannah, GA, USA aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer International Publishing 22/5(2015-10-01), 1089-1114 1021-9722 22:5<1089 2015 22 30 SWISSBIB 605496471