EUDML

Sobolev’s original definition of his spaces $L^{m, p} (Ω)$ is revisited. It only assumed that $Ω \subseteq ℝ^{n}$ is a domain. With elementary methods, essentially based on Poincare’s inequality for balls (or cubes), the existence of intermediate derivates of functions $u \in L^{m, p} (Ω)$ with respect to appropriate norms, and equivalence of these norms is proved.

On general solvability properties of $p$ -Lapalacian-like equations

Pavel Drábek; Christian G. Simader — 2002

Mathematica Bohemica

We discuss how the choice of the functional setting and the definition of the weak solution affect the existence and uniqueness of the solution to the equation $- Δ_{p} u = f in Ω,$ where $Ω$ is a very general domain in $ℝ^{N}$ , including the case $Ω = ℝ^{N}$ .

Higher regularity of weak solutions of strongly nonlinear elliptic equations

Simader, Christian G. — 1986

Equadiff 6

The weak Dirichlet and Neumann problem for the Laplacian in $L^{q}$ for bounded and exterior domains. Applications

Simader, Christian G. — 1990

Nonlinear Analysis, Function Spaces and Applications

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Remarks on essential self-adjointness of Schrödinger operators with singular electrostatic potentials.

Bemerkungen über Schrödinger-Operatoren mit stark singulären Potentialen.

Über schwache Lösungen des Dirichletproblems für streng nichtlineare elliptische Differentialgleichungen.

Essential Self-Adjointness of Schrödinger Operators Bounded from Below.

An Elementary Proof of Harnack's Inequality for Schrödinger Operators and Related Topics.

Über eine Koerzitivitätsgleichung in ... .

A second look on definition and equivalent norms of Sobolev spaces

On general solvability properties of $p$ -Lapalacian-like equations

Higher regularity of weak solutions of strongly nonlinear elliptic equations

The weak Dirichlet and Neumann problem for the Laplacian in $L^{q}$ for bounded and exterior domains. Applications