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Displaying similar documents to “On an over-determined problem of free boundary of a degenerate parabolic equation”

Large time behavior of solutions to a class of doubly nonlinear parabolic equations

Hua Shui Zhan (2008)

Applications of Mathematics

Similarity:

We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation u t = div ( u m - 1 | D u | p - 2 D u ) - u q with an initial condition u ( x , 0 ) = u 0 ( x ) . Here the exponents m , p and q satisfy m + p 3 , p > 1 and q > m + p - 2 .

A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Luisa Fattorusso (2008)

Czechoslovak Mathematical Journal

Similarity:

Let Ω be a bounded open subset of n , n > 2 . In Ω we deduce the global differentiability result u H 2 ( Ω , N ) for the solutions u H 1 ( Ω , n ) of the Dirichlet problem u - g H 0 1 ( Ω , N ) , - i D i a i ( x , u , D u ) = B 0 ( x , u , D u ) with controlled growth and nonlinearity q = 2 . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.

Differentiability of weak solutions of nonlinear second order parabolic systems with quadratic growth and nonlinearity q 2

Luisa Fattorusso (2004)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let Ω be a bounded open subset of n , let X = ( x , t ) be a point of n × N . In the cylinder Q = Ω × ( - T , 0 ) , T > 0 , we deduce the local differentiability result u L 2 ( - a , 0 , H 2 ( B ( σ ) , N ) ) H 1 ( - a , 0 , L 2 ( B ( σ ) , N ) ) for the solutions u of the class L q ( - T , 0 , H 1 , q ( Ω , N ) ) C 0 , λ ( Q ¯ , N ) ( 0 < λ < 1 , N integer 1 ) of the nonlinear parabolic system - i = 1 n D i a i ( X , u , D u ) + u t = B 0 ( X , u , D u ) with quadratic growth and nonlinearity q 2 . This result had been obtained making use of the interpolation theory and an imbedding theorem of Gagliardo-Nirenberg type for functions u belonging to W 1 , q C 0 , λ .