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Register a new user$W^{1,1}_0(Omega)$ in some borderline cases of elliptic equations with degenerate coercivity
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We study a degenerate elliptic equation, proving existence results of distributional solutions in some borderline cases.
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We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a unique W^{1,1}_0 distributional solution under suitable summability assumptions on the source in Lebesgue spaces. Moreover, we prove that our problem has no solution if the source is a Radon measure concentrated on a set of zero harmonic capacity.
In this paper we study the existence of solutions of thedegererate elliptic system.
We study a degenerate elliptic equation, proving the existence of a W^{1,1}_0 distributional solution.
We study an integral non coercive functional defined on H^1_0, proving the existence of a minimum in W^{1,1}_0.
We consider a boundary value problem in a bounded domain involving a degenerate operator of the form $$L(u)=-textrm{div} (a(x) abla u)$$ and a suitable nonlinearity $f$. The function $a$ vanishes on smooth 1-codimensional submanifolds of $Omega$ where it is not allowed to be $C^{2}$. By using weighted Sobolev spaces we are still able to find existence of solutions which vanish, in the trace sense, on the set where $a$ vanishes.
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