Nonlinear potentials and quasilinear PDE’s. (English) Zbl 0857.35046

Malý, Jan

Král, Josef (ed.) et al., Potential theory – ICPT ’94. Proceedings of the international conference, Kouty, Czech Republic, August 13–20, 1994. Berlin: deGruyter. 103-128 (1996).

Summary: Quasilinear elliptic equations of type \(-\text{div } A(x,u,\nabla u)+B(x,u,\nabla u)=\mu\) are studied. Estimates of subsolutions and supersolutions in terms of integrals \[ \int^R_0 \biggl({{\text{cap}_p (B(z,r)\setminus \Omega,r)}\over{r^{n-p}}} \biggr)^{1/(p-1)} {dr\over r} \] (Wiener type conditions) and \(\int^R_0 ({{\mu(B(x,r))} \over{r^{n-p}}})^{1/(p-1)} {dr\over r}\) are discussed.
For the entire collection see [Zbl 0844.00023].

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
31C15	Potentials and capacities on other spaces
35J70	Degenerate elliptic equations
35A35	Theoretical approximation in context of PDEs

Keywords:

\(p\)-Laplacian; Wiener type conditions; subsolutions; supersolutions