Problems involving $p$-Laplacian type equations and measures

Tero Kilpeläinen

Displaying similar documents to “Problems involving $p$ -Laplacian type equations and measures”

Problems involving $p$ -Laplacian type equations and measures

Kilpeläinen, Tero

Similarity:

On the fusion problem for degenerate elliptic equations II

Stephen M. Buckley, Pekka Koskela (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $F$ be a relatively closed subset of a Euclidean domain $Ω$ . We investigate when solutions $u$ to certain elliptic equations on $Ω ∖ F$ are restrictions of solutions on all of $Ω$ . Specifically, we show that if $\partial F$ is not too large, and $u$ has a suitable decay rate near $F$ , then $u$ can be so extended.

Harmonic spaces associated with adjoints of linear elliptic operators

Peter Sjögren (1975)

Annales de l'institut Fourier

Similarity:

Let $L$ be an elliptic linear operator in a domain in $R^{n}$ . We imposse only weak regularity conditions on the coefficients. Then the adjoint $L^{*}$ exists in the sense of distributions, and we start by deducing a regularity theorem for distribution solutions of equations of type $L^{*} u =$ given distribution. We then apply to $L^{*}$ R.M. Hervé’s theory of adjoint harmonic spaces. Some other properties of $L^{*}$ are also studied. The results generalize earlier work of the author.

Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential

Darko Žubrinić (2003)

Czechoslovak Mathematical Journal

Similarity:

We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of $p$ -Laplacian type. If $p < γ < N$ and the right-hand side is a Radon measure with singularity of order $γ$ at $x_{0} \in Ω$ , then any supersolution in $W_{l o c}^{1, p} (Ω)$ has singularity of order at least $\frac{(γ - p)}{(p - 1)}$ at $x_{0}$ . In the proof we exploit a pointwise estimate of $𝒜$ -superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.

Displaying similar documents to “Problems involving p -Laplacian type equations and measures”