A Necessary Condition to Regularity of a Boundary Point for a Degenerate Quasilinear Parabolic Equation | Zendy

Salvatore Leonardi | Zendy; Igor I. Skrypnik | Zendy

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A Necessary Condition to Regularity of a Boundary Point for a Degenerate Quasilinear Parabolic Equation

Author(s) -

Salvatore Leonardi,

Igor I. Skrypnik

Publication year - 1996

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/693

Subject(s) - degenerate energy levels , mathematical analysis , parabolic partial differential equation , point (geometry) , boundary (topology) , mathematics , boundary value problem , physics , partial differential equation , geometry , quantum mechanics

We shall study the behaviour of solutions of the equation au _-ai (x,t,u, ±) = ao (x,t,11, ) ( ( X, t) E QT = fix (0, T' )) at i=1 axi at a point (xo,to) E ST Ôfl x (0, T). Inded we establish a necessary condition to the regularity of a boundary point of the cylindrical domain QT extending the analogous result from paper [13] to the degenerate case. The degeneration is given by weights (depending on the space variable) from a suitable Muchenhoupt class. It is important to note that the coefficients of the equation depend on time too.

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