Summary
Weighted a priori bounds for the equation Δu+(μ/y)uy=f(μ>0), in the halfplane y>0, are proved. If p>1, 0<α+p−1<1+μ, u has bounded support and yµuy→0 (as y→0+), then the Lp norms of uαu and yα∥D2u∥ are bounded by the Lp norm of yαf. A boundary value problem in a rectangle is also studied in the appropriate weighted Sobolev class.
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Lavoro eseguito nell'ambito dell'Istituto di Analisi Globale ed Applicazioni del C.N.R.
Lavoro eseguito nell'ambito del Gruppo Nazionale di Analisi Funzionale ed Applicazioni del C.N.R.
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Arena, O., Manselli, P. Bounds for the nonhomogeneous GASPT equation. Annali di Matematica pura ed applicata 136, 153–182 (1984). https://doi.org/10.1007/BF01773382
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DOI: https://doi.org/10.1007/BF01773382