Lineare partielle Differentialgleichungen 2. Ordnung

Elliptisch: Laplace auf Einheitskreis

Simplify[(∫_0^(2π))(( (1/2)Sin[3t]+(1/8)Cos[17t])/((((x-Cos[t]))^2)+(((y-Sin[t]))^2)))\[DifferentialD]t,Abs[x+I y]<1]

uu[x_,y_]:=((1-(x^2)-(y^2))/(2π))(-(1/(4 (-1+(x^2)+(y^2))))π ((x^17)+12 (x^2) y-136 (x^15) (y^2)-4 (y^3)+2380 (x^13) (y^4)-12376 (x^11) (y^6)+24310 (x^9) (y^8)-19448 (x^7) (y^10)+6188 (x^5) (y^12)-680 (x^3) (y^14)+17 x (y^16)))

uu[x,y]//Simplify

uu[.9,.9]

Plot3D[uu[x,y],{x,-1,1},{y,-1,1},RegionFunction->Function[{x,y},x^2+y^2<1],BoxRatios->Automatic,AxesLabel->Automatic]

ParametricPlot3D[{{Cos[t],Sin[t], (1/2)Sin[3t]+(1/8)Cos[17t]},{Cos[t],Sin[t],0}},{t,0,2π},BoxRatios->Automatic,AxesLabel->{"x","y","z"}]