We extend the refined maximum principle in [H. Berestycki, L. Nirenberg, S.R.S. Varadhan, The principal eigenvalue and the maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math. 47 (1994) 47-92] to degenerate elliptic and parabolic equations with unbounded coefficients. Then we discuss the well-posedness of the corresponding Dirichlet boundary value problems.
On the refined maximum principle for degenerate elliptic and parabolic problems / F. Punzo, A. Tesei. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 70:8(2009), pp. 3047-3055.
On the refined maximum principle for degenerate elliptic and parabolic problems
F. PunzoPrimo
;
2009
Abstract
We extend the refined maximum principle in [H. Berestycki, L. Nirenberg, S.R.S. Varadhan, The principal eigenvalue and the maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math. 47 (1994) 47-92] to degenerate elliptic and parabolic equations with unbounded coefficients. Then we discuss the well-posedness of the corresponding Dirichlet boundary value problems.
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