Nonexistence of Solutions for Quasilinear Elliptic Equations with p-growth in the Gradient
Southwest Texas State University, Department of Mathematics
We study the nonexistence of weak solutions in W1,p loc (Ω) for a class of quasilinear elliptic boundary-value problems with natural growth in the gradient. Nonsolvability conditions involve general domains with possible singularities of the right-hand side. In particular, we show that if the data on the right-hand side are sufficiently large, or if inner radius of Ω is large, then there are no weak solutions.
Quasilinear elliptic, Existence, Nonexistence, Geometry of domains
Zubrinic, D. (2002). Nonexistence of solutions for quasilinear elliptic equations with p-growth in the gradient. <i>Electronic Journal of Differential Equations, 2002</i>(54), pp. 1-8.