Abstract

We prove some stability results on sequences of solutions of weighted elliptic equations such as −div(s(x)∣∇un∣p−2 ∇un)=fn(x) ,-{\rm div}(s(x)|\nabla u_n |^{p-2}\,\nabla u_n) = f_n(x)\,, under some assumptions on the convergence of the sequence {fn}\{f_n\} (either weak or strong in some Lebesgue space). Here s(x)s(x) is a positive weight belonging to the Sobolev space W1,p(Ω)W^{1,p}(\Omega).

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Keywords

  • Weighted elliptic equations
  • stability of solutions
  • weak and strong convergence

Mathematics Subject Classification

35J15, 35J60, 35J66

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Suggested citation

L. Boccardo, P. Imparato, L. Orsina. “Stability of the Solutions of Nonlinear Weighted Elliptic Equations Without the Weighted Sobolev Spaces Framework.” Journal of Convex Analysis 33 (2026), No. 3&4, 629–635. https://doi.org/10.68381/jca33039

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.