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On convexity and starshapedness of level sets for some nonlinear elliptic and parabolic problems on convex rings

Díaz Díaz, Jesús Ildefonso and Kawohl, B. (1993) On convexity and starshapedness of level sets for some nonlinear elliptic and parabolic problems on convex rings. Journal of Mathematical Analysis and Applications, 177 (1). pp. 263-286. ISSN 0022-247X

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Abstract

"We consider some degenerate parabolic problems on a convex (or starshaped) ring. We prove that if the initial data have convex (or starshaped) level sets, then the solution u(t,⋅) has the same property for any positive t. Similar results are shown for the corresponding stationary problems. Our results imply in particular the convexity (or starshapedness) of certain free boundaries. Other nonlinear parabolic problems are also discussed.''

Item Type:Article
Uncontrolled Keywords:porous-medium equation; geometrical properties; obstacle problem; free-boundary; diffusion; stabilization; continuity; regularity; concavity; support
Subjects:Sciences > Mathematics > Differential equations
ID Code:16178
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