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Existence of bounded solutions for some degenerated quasilinear elliptic equations

Summary

We prove the existence of bounded solutions in L (Ω) of degenerate elliptic boundary value problems of second order in divergence form with natural growth in the gradient. For the Dirichlet problem our results cover also unbounded domains Ω.

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Work performed under the auspicies of G.N.A.F.A. of the C.N.R., partially supported by M.P.I. of Italy (40%).

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Drábek, P., Nicolosi, F. Existence of bounded solutions for some degenerated quasilinear elliptic equations. Annali di Matematica pura ed applicata 165, 217–238 (1993). https://doi.org/10.1007/BF01765850

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Keywords

  • Elliptic Equation
  • Dirichlet Problem
  • Divergence Form
  • Unbounded Domain
  • Elliptic Boundary