Some notes on the method of moving planes. (English) Zbl 0777.35005

Summary: The author obtains a version of the sliding plane method of Gidas, Ni and Nirenberg which applies to domains with no smoothness condition on the boundary. The method obtains results on the symmetry of positive solutions of boundary value problems for nonlinear elliptic equations. We also show how our techniques apply to some problems on half spaces.


35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
Full Text: DOI


[1] DOI: 10.1007/BFb0090426
[2] Protter, Maximum principles in differential equations (1967) · Zbl 0153.13602
[3] Kinderlehrer, An introduction to variational inequalities and their applications (1980) · Zbl 0457.35001
[4] DOI: 10.1002/cpa.3160340406 · Zbl 0465.35003
[5] DOI: 10.1007/BF02571362 · Zbl 0705.35043
[6] DOI: 10.1080/03605308108820196 · Zbl 0462.35041
[7] Gilbarg, Elliptic partial differential equations of second order (1977) · Zbl 0361.35003
[8] DOI: 10.1007/BF01221125 · Zbl 0425.35020
[9] DOI: 10.1112/plms/s3-53.3.429 · Zbl 0572.35040
[10] Holmes, Geometric functional analysis and applications (1975) · JFM 56.0079.05
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