Strongly nonlinear degenerate elliptic equations with discontinuous coefficients. II
- 19 Downloads
We use energy methods to prove the existence and uniqueness of solutions of the Dirichlet problem for an elliptic nonlinear second-order equation of divergence form with a superlinear tem [i.e., g(x, u)=v(x) a(x)⋎u⋎ p−1u,p>1] in unbounded domains. Degeneracy in the ellipticity condition is allowed. Coefficients a i,j(x,r) may be discontinuous with respect to the variable r.
KeywordsWeak Solution Open Subset Dirichlet Problem Unbounded Domain Quasilinear Elliptic Equation
Unable to display preview. Download preview PDF.
- 3.A. V. Ivanov and P. Z. Mkrtycjan “On the solvability of the first boundary value problem for certain classes of degenerating quasilinear elliptic equations of the second order,” in: O. A. Ladyzhenskaja (editor), Boundary Value Problems of Mathematical Physics, Vol. X, Issue 2, Proc. of the Steklov Inst. of Math., A. M. S. Providence (1981), pp. 11–35.Google Scholar