A transmission problem with (p, q)-Laplacian

• In this paper we consider the so-called double-phase problem where the phase transition takes place across the interface of the positive and negative phase of minimizers of the functional (Formula presented.) We prove that minimizers exist, are Hölder regular and verify (Formula presented.) in a weak sense. We also prove that their free boundary is (Formula presented.) a.e. with respect to the measure (Formula presented.) whose support is of σ-finite (Formula presented.) -dimensional Hausdorff measure.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Free boundary

Optimal regularity

Transmission problem

Publication and Content Type

ref (subject category)

art (subject category)