Rearrangements and convexity of level sets in pde

Analogously, a level surface is sometimes called an implicit surface or an isosurface the name isocontour is also used, which means a contour of equal. Moreover geometric type inequalities will be presented, such as isoperimetric or brunnminkowski inequalities, both in their classic formulation and for functionals related to such equations. Comparison results for nonlinear divergence structure. Trudinger, elliptic partial differential equations of second order, 2nd edition, berlin. Quasiconvex qc functions appear naturally in optimization, since they generalize convex functions.

Topics in geometric function theory, mcgrawhill series in higher mathematics, 1973, 5. Lecture notes in mathematics, springer verlag, 1985. Rearrangements and convexity of level sets in pde authors. Sampson on rearrangement and weighted inequalities for the fourier transform. Under suitable conditions, a level set of uis convex if and only if this quantity has the correct sign on that level set.

Sweers, on a formula for sets of constant width in 2d, comm. Rearrangements and convexity of level sets in pde it seems that youre in usa. Salani, quasiconcave envelope of a function and convexity of level sets of solutions to elliptic equations, math. Rearrangements and convexity of level sets in pde book. Rearrangements and convexity of level sets in pde book, 1985.

Contraction of convex hypersurfaces in euclidean space, calc. For example, an implicit curve is a level curve, which is considered independently of its neighbor curves, emphasizing that such a curve is defined by an implicit equation. They use then the geometrical fact that since the horizontal slices of both sets have the same measure and those of the second are balls, to deduce that the area of the boundary of the cylindrical set c. A class of monotone decreasing rearrangements sciencedirect. Kawohl rearrangements and convexity of level sets in pde. Supported in part by national science foundation grant dms1406164. Kawohl, rearrangements and convexity of level sets in pde. Bernhard kawohl, rearrangements and convexity of level sets in pde, lecture notes in mathematics, vol. Idescriptions of the available techniques to prove convexity results. Fridman, isoperimetric estimates for the first eigenvalue of the plaplace operator and the cheeger constant, comment. Some remarks about a notion of rearrangement numdam.

Pdf rearrangements and convexity of level sets in pde. We consider monotone decreasing rearrangement with respect to the finite. Strict convexity of level sets of solutions of some nonlinear elliptic equations. Inspired by work of montgomery on fourier series and donoho strak in signal processing, we investigate two families of rearrangement inequalities for the fourier transform. Kawohl, rearrangements and convexity of level sets in pde s, lecture notes in mathe.

Kawohl, rearrangements and convexity of level sets in pde, lecture notes in mathematics, vol. Convex solutions to the mean curvature flow annals of. Kawohl 1985 rearrangements and convexity of level sets in pde, lecture notes in math. Principal curvature estimates for the convex level sets of semilinear elliptic equations. Kawohl, rearrangements and convexity of level sets in pdes, lecture notes in mathe. Pdf strict convexity of level sets of solutions of some. Hardys inequality in a limiting case on general bounded.

Rearrangements and convexity of level sets in pde by bernhard kawohl, 9783540156932, available at book depository with free delivery worldwide. The convexity of levelsets of solutions for partial differential equations was. Kawohl, rearrangements and convexity of level sets in pde, lectures notes. Kawohl, rearrangements and convexity of level sets in pde, new york. A function with convex level sets but is not a convex function. Rearrangements and convexity of level sets in pde springer. Miranda, partial differential equations of elliptic type, springer verlag 1970. These sets are the sets of points who lie between the domain of the functions and. These rearrangements can also preserve or improve analytic quantities, such as the energies of functions defined on these objects.

Analogously, a level surface is sometimes called an implicit surface or an isosurface. Convexity sets differential equation maximum partial differential equation. Computing the quasiconvex envelope using a nonlocal line solver. On the convexity of a solution of liouvilles equation. Rearrangements and convexity of level sets in pde computer.

Lieb, existence and uniqueness of the minimizing solution of choquards nonlinear equation, studies in appl. Kawohl, rearrangements and convexity of level sets in pde, number 1150 in. Kawohl, rearrangements and convexity of level sets in pdes, lectures notes in mathematics 1150, springerverlag, berlin, 1985. Kennington, an improved convexity maximum principle and some applications. Kawohl, rearrangements and convexity of level sets in pde, lecture notes in math. Read the steiner rearrangement in any codimension, calculus of variations and partial differential equations on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Rearrangements and convexity of level sets in pde springerlink. Dec 29, 2012 read the steiner rearrangement in any codimension, calculus of variations and partial differential equations on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Approximate convexity principles and applications to pdes. Gradient estimates, rearrangements and symmetries giorgio talenti department of mathematics university of florence viale morgagni 67a, 504 florence, italy consider a dirichlet boundary value problem for a secondorder partial differential equation of elliptic type and suppose that estimates of the gradient of relevant solutions are in demand. Ams proceedings of the american mathematical society. Quasiconcavity, the condition that the level sets of a positive graph. Gradient estimates, rearrangements and symmetries sciencedirect. Interactions between elliptic pdes and convex geometry.

Rearrangements and convexity of level sets in pde lecture. Full text of on the fourier transform of the symmetric. Altmetric rearrangements and convexity of level sets in pde. Kennington, convexity of level curves for an initial value problem. Counterexamples to quasiconcavity for the heat equation. Principal curvature estimates for the level sets of. Kawhol, rearrangements and convexity of level sets in pde, springer lecture notes in. Rearrangements and convexity of level sets in pde published by. Rearrangements and convexity of level sets in pde core.

Kawohl, rearrangements and convexity of level sets in pde, lect. On convexity and starshapedness of level sets for some nonlinear elliptic and parabolic problems on convex rings, j. Rearrangements and convexity of level sets in pde, volume 1150 of lecture notes in mathematics. Sorry, we are unable to provide the full text but you may find it at the following locations. Kawohl, rearr angements and convexity of level sets in pde, lectures notes in math. Rearrangements and convexity of level sets in pde bernhard kawohl.

Xu, a microscopic convexity principle for the level sets of solution for nonlinear elliptic partial differential equations, to appear in indiana univ. Isuggestions of strategies to approach new or unsolved problems. Rearrangements and convexity of level sets in \rm pde. Kawhol, rearrangements and convexity of level sets in pde, springer. Kawohl, rearrangements and convexity of level sets in pde, lecture notes in mathematics vol. R e d x w gis the number of cars in the set m at time w. Variational methods for nonlinear partial differential equations by carlos tello a thesis submitted to the graduate faculty of wake forest university in partial ful llment of the requirements for the degree of master of arts mathematics december 2010 winstonsalem, north carolina approved by. Velte, buckling eigenvalues for a clamped plate embedded in an elastic medium and related questions. Epperson department of mathematics, university of new mexico, albuquerque, new mexico 871 submitted by dorothy maharam stone received january 23, 1989 we consider monotone decreasing rearrangement with respect to the finite measure dfix.

Kawohl, rearrangements and convexity of level sets in pdes, lecture notes in mathematics, springer verlag, 1985. You dont actually need logconcavity, the convexity of level sets would be enough. Kawohl, rearrangements and convexity of level sets in pdes. A function with convex level sets but is not a convex. Rearrangements and convexity of level sets in pde bernhard. Full text of on the fourier transform of the symmetric decreasing rearrangements see other formats on the fourier transform of the symmetric decreasing rearrangements philippe jaming resume.