Structure of nodal and singular sets for solutions to semilinear PDEs

来源 :2014 workshop on nonlinear evolutionary partial differential | 被引量 : 0次 | 上传用户：king4978

【摘要】

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I shall discuss issues related to the level surfaces and singular sets for solutions to semilinear problems of the type $Delta u = f(u)$,where $f$ admits disco

【作者】

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Henrik Shahgholian

【机构】

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TheRoyalInstituteofTechnology,Sweden

【出处】

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2014 workshop on nonlinear evolutionary partial differential

【发表日期】

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2014年12期

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I shall discuss issues related to the level surfaces and singular sets for solutions to semilinear problems of the type $\Delta u = f(u)$,where $f$ admits discontinuities.Across such discontinuity points the PDE changes qualitatively and therefore one may see such nodal sets as free boundaries.The kind of free boundary we obtain depends on the type of discontinuity of $f$,or more exactly it depends on the right and left limit values for $f$ at such discontinuity points.I shall present partial results as well as a program for a possible analysis of this problem.

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Structure of nodal and singular sets for solutions to semilinear PDEs

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