We investigate uniqueness for degenerate parabolic and elliptic equations in the class of solutions belonging to weighted Lebesgue spaces and not satisfying any boundary condition. The uniqueness result that we provide relies on the existence of suitable positive supersolutions of the adjoint equations. Under proper assumptions on the behavior at the boundary of the coefficients of the operator, such supersolutions are constructed, mainly using the distance function from the boundary.
Uniqueness of solutions to degenerate parabolic and elliptic equations in weighted Lebesgue spaces / F. Punzo. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 286:10(2013), pp. 1043-1054. [10.1002/mana.201200040]
Uniqueness of solutions to degenerate parabolic and elliptic equations in weighted Lebesgue spaces
F. Punzo
2013
Abstract
We investigate uniqueness for degenerate parabolic and elliptic equations in the class of solutions belonging to weighted Lebesgue spaces and not satisfying any boundary condition. The uniqueness result that we provide relies on the existence of suitable positive supersolutions of the adjoint equations. Under proper assumptions on the behavior at the boundary of the coefficients of the operator, such supersolutions are constructed, mainly using the distance function from the boundary.Pubblicazioni consigliate
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